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Find the minimum value of C = 6x + 7y Subject to the following constraints: x > 0 y > 0 4x + 3y = 24 x + 3y > 15

User YogiAR
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1 Answer

15 votes
15 votes

4x + 3y = 24

Find the x- interecpt

substitute x = 0

4(0) + 3y = 24

3y = 24

y = 8

substitute y = 0

4x + 3(0) = 24

4x = 24

x =6

The intercepts are;

(0,8) and (6, 0)

x + 3y = 15

substitute x = 0

3y = 15

y =5

substitute y=0

x= 15

The intercept is;

(0, 5) and (15, 0)

Find the point of intersection by solving;

4x + 3y = 24 and x + 3y = 15 simultaneously

4x + 3y = 24 --------------------(1)

x + 3y = 15 --------------------(2)

subtract equation (2) from equation(1)

3x = 9

Divide bothside of the equation by 3

x = 3

substitute x = 3 into into equation (2)

3 + 3y = 15

subtract 3 from bothside

3y = 15 - 3

3y = 12

Divide both-side of the equation by 3

y = 4

(3, 4)

The coordinate of the feasible regions are;

(0, 8) (3, 4) and (15, 0)

Evaluate vertex values into the function below and solve for C

C= 6x + 7y

C = 6(0) + 7(8) = 0 + 56 = 56

C = 6(3) + 7(4) = 18 + 28 = 46

C = 6(15) + 7(0) = 90 + 0 = 90

Therefore the minimum value of C = 46 at (3, 4)

User Mdec
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