A manufacturing company would like to maximize the profit of manufacturing four products.

1. A manufacturing company would like to maximize the profit of manufacturing four products.  The time in hours required for each product in each production department is tabled below, along with the profit for each product.

Product 1

Product 2

Product 3

Product 4

Department A

25

20

30

15

Department B

12

10

10

15

Department C

  8

  7

5

6

Profit

$110

$90

100

95

Currently labor assignments provide for 4800 hours in Department A, 3000 hours in Department B and 2800 hours in Department C. 

Formulate a linear programming model for the above situation by determining

(a) The decision variables.

(b) Determine the objective function. What does it represent?

(c) Determine all the constraints. Briefly describe what each constraint represents.

Hint: There are 4 variables and 3 constraints (in addition to the non-negativity constraints) for this problem.

2. Find the computer solution, including the ranging (sensitivity analysis) results, for Question 1 by using QM for Windows or Excel. Determine the optimal solution (including the decision variables and the slack/surplus variables) and optimal profit. Interpret the optimal solution and optimal profit.

3. Answer the following questions by using the ranging results (that is, the sensitivity analysis results) from Question 2. Do NOT solve the problem again by using any computer software or website.

(a) If the profit from a unit of Product 2 increases from $90 to $110, will the optimal number of units of the four products manufactured change? Will the total profit change? If they change, what will be the new total profit?

(b)The company has an opportunity to get some extra hours in Department A. What is the maximum price the company should pay for each additional hour in Department A, and how many hours should they get at that price?

(c)The company has an opportunity to get some extra hours in Department C. What is the maximum price the company should pay for each additional hour in Department C, and how many hours should they get at that price?

(d) Which department should obtain more hours to increase the profit most?

Only need help with #3