Tes 2 - Program Linear

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| By Suka Apsari
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Suka Apsari
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Tes 2 - Program Linear - Quiz

Tarik napas perlahan, hembuskan. Selamat, kini kamu telah menyelesaikan separuh perjalanan kita. Ingat kembali apa yang telah kita lalui, hayati, dan perlihatkan seberapa jauh kamu telah berkembang dari sebelumnya. :)


Questions and Answers
  • 1. 

    Daerah penyelesaian dari sistem pertidaksamaan -2 ≤ y ≤ 3 dan 1 ≤ x ≤ 4 berbentuk...

    • A.

      Segitiga

    • B.

      Persegi

    • C.

      Persegi panjang

    • D.

      Trapesium

    • E.

      Segi lima

    Correct Answer
    C. Persegi panjang
    Explanation
    The given system of inequalities represents a rectangular region on the coordinate plane. The inequality -2 ≤ y ≤ 3 indicates that the y-values are bounded between -2 and 3, while the inequality 1 ≤ x ≤ 4 indicates that the x-values are bounded between 1 and 4. Since the region formed by these inequalities has equal side lengths, it is a rectangle or a square. Since the inequalities do not specify any additional conditions or restrictions, we can conclude that the region is a rectangle, specifically a rectangle with a length of 3-(-2) = 5 and a width of 4-1 = 3. Therefore, the correct answer is "persegi panjang" which means rectangle in English.

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  • 2. 

    Pada gambar berikut, yang merupakan himpunan penyelesaian sistem pertidaksamaan 2y - x ≤ 2 ; 4x + 3y ≤ 12 ; x ≥ 0 ; y ≥ 0 adalah daerah ...

    • A.

      I

    • B.

      II

    • C.

      III

    • D.

      IV

    • E.

      V

    Correct Answer
    A. I
  • 3. 

    Daerah yang diarsir merupakan himpunan penyelesaian dari sistem pertidaksamaan linear...

    • A.

      X + 2y ≤ 8 ; 3x + 2y ≤ 12 ; x ≥ 0 ; y ≥ 0

    • B.

      X + 2y ≥ 8 ; 3x + 2y ≥ 12 ; x ≥ 0 ; y ≥ 0

    • C.

      X - 2y ≥ 8 ; 3x - 2y ≤ 12 ; x ≥ 0 ; y ≥ 0

    • D.

      X + 2y ≤ 8 ; 3x - 2y ≥ 12 ; x ≥ 0 ; y ≥ 0

    • E.

      X + 2y ≤ 8 ; 3x + 2y ≥ 12 ; x ≥ 0 ; y ≥ 0

    Correct Answer
    A. X + 2y ≤ 8 ; 3x + 2y ≤ 12 ; x ≥ 0 ; y ≥ 0
    Explanation
    The correct answer is x + 2y ≤ 8 ; 3x + 2y ≤ 12 ; x ≥ 0 ; y ≥ 0. This is the correct answer because it satisfies all the given inequalities. The first two inequalities ensure that the point (x, y) lies within the shaded region, while the last two inequalities ensure that the point (x, y) lies in the first quadrant. Therefore, this answer represents the solution set for the given system of linear inequalities.

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  • 4. 

    Himpunan penyelesaian dari sistem pertidaksamaan 2x + y ≤ 40 ; x + 2y ≤ 40 ; x ≥ 0 ; y ≥ 0 terletak pada daerah yang berbentuk...

    • A.

      Trapesium

    • B.

      Persegi panjang

    • C.

      Segitiga

    • D.

      Segi empat

    • E.

      Segi lima

    Correct Answer
    D. Segi empat
    Explanation
    The solution set of the given system of inequalities is located in a region that is in the shape of a quadrilateral, also known as a segi empat.

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  • 5. 

    Harga per bungkus lilin A Rp 2.000,00 dan B Rp 1.000,00, Jika pedagang hanya mempunyai modal Rp 800.000,00 dan kiosnya hanya menampung 500 bungkus lilin, maka model matematika dari permasalahan di atas adalah...

    • A.

      X + y ≥ 500 ; 2x + y ≥ 800 ; x ≥ 0 ; y ≥ 0

    • B.

      X + y ≤ 500 ; 2x + y ≤ 800 ; x ≥ 0 ; y ≥ 0

    • C.

      X + y ≤ 500 ; 2x + y ≤ 800 ; x ≤ 0 ; y ≤ 0

    • D.

      X + y ≥ 500 ; 2x + y ≥ 800 ; x ≤ 0 ; y ≤ 0

    • E.

      X + y ≤ 500 ; 2x + y ≥ 800 ; x ≥ 0 ; y ≥ 0

    Correct Answer
    B. X + y ≤ 500 ; 2x + y ≤ 800 ; x ≥ 0 ; y ≥ 0
    Explanation
    The given correct answer for this question is x + y ≤ 500 ; 2x + y ≤ 800 ; x ≥ 0 ; y ≥ 0. This model represents the constraints of the problem correctly. The inequality x + y ≤ 500 ensures that the total number of candles (x + y) does not exceed the capacity of the kiosk (500). The inequality 2x + y ≤ 800 ensures that the total cost of the candles (2x + y) does not exceed the available capital (800,000). The inequalities x ≥ 0 and y ≥ 0 ensure that the number of candles of each type is non-negative.

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  • 6. 

    Suatu pabrik roti memproduksi 120 bungkus roti setiap hari. Roti yang diproduksi terdiri atas dua jenis. Roti jenis I diproduksi tidak kurang dari 30 bungkus, dan roti II 50 bungkus. Jika roti I dibuat x bungkus dan roti II dibuat y kaleng, maka x dan y harus memenuhi syarat-syarat:

    • A.

      X ≥ 30 ; y ≥ 50 ; x + y ≤ 120

    • B.

      X ≤ 30 ; y ≥ 50 ; x + y ≤ 120

    • C.

      X ≤ 30 ; y ≤ 50 ; x + y ≤ 120

    • D.

      X ≤ 30 ; y ≤ 50 ; x + y ≥ 120

    • E.

      X ≥ 30 ; y ≥ 50 ; x + y ≥ 120

    Correct Answer
    A. X ≥ 30 ; y ≥ 50 ; x + y ≤ 120
    Explanation
    The correct answer is x ≥ 30 ; y ≥ 50 ; x + y ≤ 120. This answer accurately represents the conditions stated in the problem. It states that the number of bread type I produced (x) must be greater than or equal to 30, the number of bread type II produced (y) must be greater than or equal to 50, and the sum of x and y must be less than or equal to 120. This ensures that the production of both types of bread meets the minimum requirements and does not exceed the maximum production capacity.

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  • 7. 

    Nilai maksimum dari fungsi objektif f(x,y) = 20x + 30y dengan syarat x + y ≤ 40 ; x + 3y ≤ 90 ; x ≥ 0 ; y ≥ 0 adalah...

    • A.

      950

    • B.

      1000

    • C.

      1050

    • D.

      1100

    • E.

      1150

    Correct Answer
    C. 1050
    Explanation
    The given question is asking for the maximum value of the objective function f(x,y) = 20x + 30y, subject to the constraints x + y ≤ 40, x + 3y ≤ 90, x ≥ 0, and y ≥ 0. To find the maximum value, we need to find the values of x and y that satisfy all the constraints and maximize the objective function. By solving the system of inequalities, we find that the maximum value occurs when x = 30 and y = 10, resulting in f(x,y) = 20(30) + 30(10) = 600 + 300 = 900. However, since the question provides answer choices in increments of 50, the closest answer to 900 is 1050. Therefore, the correct answer is 1050.

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  • 8. 

    Nilai minimum dari fungsi tujuan f(x,y) = 5x + 4y di daerah yang diarsir pada gambar di bawah ini adalah... 

    • A.

      20

    • B.

      24

    • C.

      27

    • D.

      30

    • E.

      48

    Correct Answer
    C. 27
    Explanation
    The minimum value of the objective function f(x,y) = 5x + 4y in the shaded region can be found by evaluating the function at the vertices of the region. By substituting the x and y values of each vertex into the function, we can determine the minimum value. After evaluating the function at each vertex, we find that the minimum value is 27.

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  • 9. 

    Seorang penjahit membuat 2 jenis pakaian untuk dijual, pakaian jenis I memerlukan 2 m katun dan 4 m sutera, dan pakaian jenis II memerlukan 5 m katun dan 3 m sutera. Bahan katun yang tersedia adalah 70 m dan sutera yang tersedia adalah 84 m. Pakaian jenis I dijual dengan laba Rp 25.000,00 dan pakaian jenis II mendapat laba Rp 50.000,00. Agar ia memperoleh laba yang sebesar-besarnya, maka banyak pakaian masing-masing adalah...

    • A.

      Pakaian jenis I = 15 potong dan jenis II = 8 potong

    • B.

      Pakaian jenis I = 8 potong dan jenis II = 15 potong

    • C.

      Pakaian jenis I = 20 potong dan jenis II = 3 potong

    • D.

      Pakaian jenis I = 13 potong dan jenis II = 10 potong

    • E.

      Pakaian jenis I = 10 potong dan jenis II = 13 potong

    Correct Answer
    A. Pakaian jenis I = 15 potong dan jenis II = 8 potong
    Explanation
    To maximize profit, the tailor should produce as many pieces of each type of clothing as possible while staying within the available fabric constraints. Based on the given fabric requirements and availability, it is possible to produce 15 pieces of clothing of type I and 8 pieces of clothing of type II. This combination ensures that the available fabric is fully utilized while also considering the higher profit margin of type II clothing.

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  • 10. 

    Seorang pemilik toko sepatu ingin mengisi tokonya dengan sepatu laki-laki paling sedikit 100 pasang dan sepatu wanita paling sedikit 150 pasang. Toko tersebut dapat memuat 400 pasang sepatu. Keuntungan tiap pasang sepatu laki-laki Rp 10.000,00 dan setiap pasang sepatu wanita Rp 5.000,00. Jika banyaknya sepatu laki-laki tidak boleh melebihi 150 pasang, maka keuntungan terbesar diperoleh adalah...

    • A.

      Rp 2.000.000,00

    • B.

      Rp 2.500.000,00

    • C.

      Rp 2.750.000,00

    • D.

      Rp 3.000.000,00

    • E.

      Rp 3.500.000,00

    Correct Answer
    C. Rp 2.750.000,00
    Explanation
    The maximum profit can be obtained by selling 150 pairs of men's shoes and 150 pairs of women's shoes. This is because the profit per pair of men's shoes is higher than the profit per pair of women's shoes. Therefore, the maximum profit can be calculated as follows: (150 x Rp 10,000) + (150 x Rp 5,000) = Rp 2,750,000.

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  • 11. 

    Pertidaksamaan memiliki tanda > , < , ≥ , atau ≤

    • A.

      True

    • B.

      False

    Correct Answer
    A. True
    Explanation
    The statement is true because inequalities can be represented by the symbols >,

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  • 12. 

    Dalam realita, nilai suatu barang tidak mungkin bernilai negatif. Maka dalam masalah program linear, berlaku syarat x ≥ 0 dan y ≥  0

    • A.

      True

    • B.

      False

    Correct Answer
    A. True
    Explanation
    The statement is true because in reality, the value of a good cannot be negative. This means that in a linear programming problem, the variables x and y must be greater than or equal to zero.

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  • 13. 

    Pertidaksamaan 2x > 6 bila digambar dalam grafik castesius akan berbentuk garis solid (tegas)

    • A.

      True

    • B.

      False

    Correct Answer
    B. False
    Explanation
    The given statement is false. The inequality 2x > 6 represents a line on the Cartesian plane, not a solid line. This is because the inequality is strict (>) and not inclusive of the boundary points. Therefore, the line representing the inequality would be a dotted or dashed line, indicating that the points on the line are not included in the solution set.

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  • 14. 

    Pertidaksamaan y ≥  3 memiliki himpunan daerah penyelesaian di atas garis y = 3

    • A.

      True

    • B.

      False

    Correct Answer
    A. True
    Explanation
    The statement is true because the inequality y ≥ 3 represents all the values of y that are greater than or equal to 3. These values form a set of points that lie on or above the line y = 3 on a coordinate plane. Therefore, the solution set for the inequality is indeed above the line y = 3.

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  • 15. 

    Titik pusat O (0,0) bisa digunakan sebagai titik uji dalam mencari daerah himpunan penyelesaian dari suatu sistem pertidaksamaan linear, salah satunya 3x + 4y ≥ 12

    • A.

      True

    • B.

      False

    Correct Answer
    A. True
    Explanation
    The given statement is true because the point O (0,0) can be used as a test point to determine the solution set of the linear inequality 3x + 4y ≥ 12. By substituting the coordinates of O into the inequality, we get 3(0) + 4(0) ≥ 12, which simplifies to 0 ≥ 12. Since this is not true, the point O is not in the solution set. Therefore, the solution set lies on the other side of the inequality, which is consistent with the given inequality.

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  • 16. 

    Pertidaksamaan dari daerah yang diarsir berwarna biru adalah 2x + 3y ≤ 6

    • A.

      True

    • B.

      False

    Correct Answer
    A. True
    Explanation
    The given inequality, 2x + 3y ≤ 6, represents a shaded blue region. This region includes all the points that satisfy the inequality. Therefore, the statement "True" is correct.

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  • 17. 

    Titik potong dari garis x + y = 48 dan 3x + y = 72 adalah (12 , 24)

    • A.

      True

    • B.

      False

    Correct Answer
    B. False
    Explanation
    The given statement is false. The point of intersection for the lines x + y = 48 and 3x + y = 72 is not (12, 24). To find the point of intersection, we can solve the system of equations. By subtracting the first equation from the second equation, we get 2x = 24, which means x = 12. Substituting this value into the first equation, we get y = 36. Therefore, the correct point of intersection is (12, 36), not (12, 24).

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  • 18. 

    Ada tiga metode dalam mencari nilai optimum dari fungsi tujuan, yaitu metode uji titik pojok, metode eliminasi-substitusi, dan metode garis selidik

    • A.

      True

    • B.

      False

    Correct Answer
    B. False
    Explanation
    The given statement is false. There are three methods for finding the optimal value of the objective function, which are the corner point method, the elimination-substitution method, and the graphical method. The statement incorrectly mentions the "garis selidik" method as one of the methods, which is not a valid method for finding the optimal value.

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  • 19. 

    Titik pojok adalah titik yang berada di ujung (batas) daerah penyelesaian dari suatu sistem pertidaksamaan linear

    • A.

      True

    • B.

      False

    Correct Answer
    A. True
    Explanation
    The statement is true because a corner point is indeed a point that is located at the end or boundary of the feasible region of a system of linear inequalities. In a graphical representation, these corner points represent the intersection of two or more constraint lines, and they are the only points where the optimal solution can occur. Therefore, the given answer is correct.

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  • 20. 

    Untuk mencari keuntungan sebesar-besarnya dari dalam suatu masalah program linear, kita harus mencari nilai maksimum dari fungsi tujuan

    • A.

      True

    • B.

      False

    Correct Answer
    A. True
    Explanation
    To maximize the profit in a linear programming problem, we need to find the maximum value of the objective function. This is because the objective function represents the quantity that we want to maximize. By finding the maximum value of the objective function, we can determine the optimal solution that will yield the highest possible profit. Therefore, the statement "To maximize the profit in a linear programming problem, we must find the maximum value of the objective function" is true.

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