Question 1. A 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.

Question 4. TP Inc. is a small company specializes in supplying toilet paper to small businesses, offices, universities, restaurants, and other similar establishments in the city of San Antonio. TP Inc. purchases their stock from brand-name toilet paper manufacturers and has significant limitations on its ability to carry an exceptionally large inventory. Despite the small business style, the company is immensely popular and gets enough clients that the demand is not deterministic in nature, but instead, follows a probabilistic pattern. The Manager of TP Inc. would like a recommendation on how many packages of toilet paper to order and when to order in an effort to minimize the inventory costs. You are provided the following pertinent information regarding the company and costs. Answer questions (a.), (b.) and (c.) given below

Ordering Cost is $100.00 per order

Cost of each package of toilet paper is $9.00 per box for TP Inc.

The company uses a 25% annual holding cost rate for its inventory

The lead time for a new order of toilet paper is 8 days

Sales data indicate that the demand during 8-day lead time follows a normal probability distribution with a weekly mean of 750 boxes and a standard deviation per week of 80 boxes.

The number of working days per year is 330

Acceptable probability of a stock-out is 1% or 0.01.

1.What is the current EOQ?

2.What is the current Reorder point?

3.The manager is also considering increasing the risk of stockouts from 1% to 10%. Do you think that would help him reduce costs? Explain why.