Question

Please please help me with this problem please

Answer 1

Answer:

C = 19 is the minimum value

Step-by-step explanation:

Sketch the inequalities using

4x + 3y = 29

with x- intercept = (7.25, 0) and y- intercept = (0, $\frac{29}{3}$)

x + 2y = 11

with x- intercept = (11, 0) and y- intercept = (0. 5.5)

Solve 4x + 3y and x + 2y = 11 simultaneously to find

Point of intersection = (5, 3)

The vertices of the feasible region are

(0, $\frac{29}{3}$), (5, 3), (11, 0)

Evaluate the objective function C = 2x + 3y at each of the vertices

(0, $\frac{29}{3}$) → C = 0 + 29 = 29

(5, 3) → C = 2(5) + 3(3) = 10 + 9 = 19 ← minimum value

(11, 0) → C = 2(11) + 0 = 22

Minimum value is C = 19 when x = 5 and y = 3