5. Given the following linear programming model, identify the optimal solution.

Maximize Z = $18x1 + $14x2

Subject to: 1) 4x1 + 2x2

2) 2x1 + 6x2

x1, x2 = 0

a) No Solution

b) x1 = 5, x2 = 6, Z = 174

c) x1 = 30, x2 = 1, Z = 554

d) x1 = 15, x2 = 5, Z = 340

e) x1 = 18, x2 = 4, Z

1. The production manager for Beer etc. produces 2 kinds of beer: light (L) and dark (D). Two

resources used to produce beer are malt and wheat. He can obtain at most 4800 oz of malt per

week and at most 3200 oz of wheat per week respectively. Each bottle of light beer requires 12

oz of malt and 4 oz of wheat, while a bottle of dark beer uses 8 oz of malt and 8 oz of wheat.

Profits for light beer are $2 per bottle, and profits for dark beer are $1 per bottle. If the

production manager decides to produce of 0 bottles of light beer and 400 bottles of dark beer,

it will result in slack of

A) malt only

B) wheat only

C) both malt and wheat

D) neither malt nor wheat

Write the formulation for this linear program And Explain

2. Consider the following linear programming problem:

Max Z = $30x + $40y

Subject to: 16x + 10y 80

0.8x + 2y 8

x, y 0

Determine the values for x and y that will maximize revenue. Show by Graph.

3. What combination of x and y will provide a feasible solution and a minimum objective

function value for the following problem?

Min Z = 3x + 15y

(1) 2x + 4y 12

(2) 5x + 2y 10

a) x = 0; y = 3

b) x = 0; y = 5

c) x = 5; y = 0

d) x = 6; y = 0

e) x = 4; y = 1

Show by Graph the optimal solution,. Explain in detail of your work

4. Max Z = 5x1 + 3x2

Subject to: 6x1 + 2x2 18

15x1 + 20x2 60

x1, x2 0

Find the optimal profit and the values of x1 and x2 at the optimal solution .Use Graph to estimate the Profit;

Explain in detail of your work