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22 March, 05:17

By graphing the system of constraints, find the values o f x and y that minimize the objective function.

x+2y=>8

x=>2

y=>0

minimum for C=x+3y

A. (8,0)

B. (2,3)

C. (0,10)

D. (10,0)

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Answers (2)
  1. 22 March, 07:04
    0
    Graph the inequalities to find the vertices of the shaded region: (2, 3) and (8, 0).

    Now, evaluate the the function C = x + 3y at those vertices to find the minimum value.

    C = x + 3y at (2, 3) ⇒ C = (2) + 3 (3) ⇒ C = 2 + 9 ⇒ C = 11

    C = x + 3y at (8, 0) ⇒ C = (8) + 3 (0) ⇒ C = 8 + 0 ⇒ C = 8

    The minimum value occurs at (8, 0) with a minimum of C = 8

    Answer: A
  2. 22 March, 07:20
    0
    Option (A)

    Step-by-step explanation:

    Here, x + 2y = 8

    c=x+3y

    x≥2

    y≥0

    By considering the options (A) and (B)

    For option (A)

    x=8 and y=0

    x+2y=8

    put values of x and y in equation

    8+2*0=8, which satisfies the equation

    now c = 8+3*0=8

    Now, for option (B)

    x=2 and y=3

    x+2y=8

    put values of x and y

    2+2*3=8, which satisfies the equation.

    now c = 2+3*3=11

    As we have to find the minimum value of c.

    hence we take c=8

    Hence, option (A) is correct.
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