Question

- Refer to the Par Insights, Inc. example in your textbook. A competitor firm DLS Apps, Inc. decides to enter the market for apps made for teenagers and children. Their Production Supervisor analyzed each of the operations and concluded that if the company produces apps for children, each app would require 8 hours in the theme creation department, 12 hours in the graphics and imaging department, 4 hours in the educational content department, 6 hours in the coding department, and 5 hours in the testing and launching department. On the other hand, each app for teenagers would require 4 hours in the theme creation department, 15 hours in the graphics and imaging department, 15 hours in the educational content department, 10 hours in the coding department, and 2 hours in the testing and launching department. After studying the departmental workload projections, the Production Supervisor estimates that 100 hours for theme creation, 250 hours for graphics and imaging, 200 hours for the educational content creation, 150 hours of coding and 50 hours for the testing and launching are available for the production of the new apps during the next four months. The accounting department analyzed the costs based on the production data and overheads and arrived at prices for the apps that will result in a profit contribution of $10,000 per children’s app and $15,000 per teenager app produced. The CEO asserts that to be successful in the long run, at least 5 children’s apps must be launched in the next four months. The management is trying to identify how many apps of each type should they launch in the next four months and have hired you to help them figure out what the optimal solution would be and what the expected profits would be.

1. Write out the Linear Program (equations)

2. Provide the optimal solution, either graphically or by using Excel Solver. What is the total expected profit? How many apps of each type would you recommend that they make?

3. Identify which constraints are binding.

4. Which department has the highest slack? How much?

5. If the company was able to obtain 5 more hours in the coding department, would the profit change? Explain why or why not.

Answer 1

1.

The LP can be written as

X = number of children’s app

Y = number of teenager’s app

Maximize 10000X + 15000Y

Subject to

8X + 4Y <= 100

12X + 15Y <= 250

4X + 15Y <= 200

6X + 10Y <= 150

5X + 2Y <= 50

X, Y >= 0

2.

The model is shown below

The formulas are shown below

The solver parameters are shown below

The result is shown below

The sensitivity analysis is shown below.

The optimal solution is to make 5.26 children’s app and 11.84 teenager’s app. The total profit that can be earned is 230263.15.

3.

The binding constraints are coding and testing hours.

4.

The theme design department has the highest slack. It is 100-89.47 = 10.53 hours

5.

Yes the profit will change. The coding hours is a binding constraint. This means for any increase in the available RHS, the solution will change.