Question

Please please help me out with this!!!!!!!!!

Answer 1

C = 46

Explanation:

Sketch the inequalities

4x + 3y = 24

with x- intercept = (6, 0) and y- intercept = (0, 8)

x + 3y = 15

with x- intercept = (15, 0) and y- intercept = (0, 5)

Solve 4x + 3y = 24 and x + 3y = 15 simultaneously to find

point of intersection = (3, 4)

The vertices of the feasible region are then

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

Evaluate the objective function C = 6x + 7y at each of these vertices.

(0, 8) → C =6(0) + 7(8) = 0 + 56 = 56

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

(3, 4) → C = 6(3) + 7(4) = 18 + 28 = 46 ← minimum value

Minimum value is C = 46 when x = 3 and y = 4

Answer 2

The minimum value for C is 46.

Explanation:

First solve for x using the last inequality:

x + 3y >= 15

x >= 15 - 3y

Now, substitute and solve for x:

4x + 3y >= 24

4(15 - 3y) + 3y >= 24

60 - 12y + 3y >= 24

-9y >= -36

y >= 4

Substitute 4 for y and solve for x:

x + 3y >= 15

x + 3(4) >= 15

x + 12 >= 15

x >= 3

Proof:

4x + 3y >= 24

4(3) + 3(4) >= 24

12 + 12 >= 24

24 >= 24

Therefore the minimum value of C is:

C = 6x + 7y

C = 6(3) + 7(4)

C = 18 + 28 = 46

Hope this Helps! Have an Awesome Day!! (-: