Pen production problem using Linear Programming technique

OPRE 315: Homework 3

1. The Charm City Manufacturing makes four models of ball point pens. Requirements for each lot of pens for each model are given below.

Economy
Model Super
Model Luxury
Model Premium Model Available
Plastic 3 4 4 4 100 units
Ink Assembly 3 4 4 6 120 units
Molding Time 4 3 5 8 140 hours

The profit for the economy model is $800 per lot. The profit for the super model is $1200 per lot. The profit for the luxury model is $1200 per lot and the profit for the premium model is $1400 per lot. How many lots of each model should the company manufacture to maximize the total profit?

Formulate a linear programming model for this problem by determining
(a) The decision variables.
(b) The objective function.
(c) All the constraints.

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

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

(a) If the profit from a lot of the premium model increases from $1400 to $1600, will the optimal number of lots of the four models produced change? Will the total profit change? If they change, what will be the new optimal solution and the new total profit?
(b) The Charm City has an opportunity to buy some extra amount of plastic. What is the maximum price the company should pay for each unit of additional plastic, and how many units of plastic should they buy at that price?
(c) The Charm City has an opportunity to obtain some extra hours of molding time. What is the maximum price the company should pay for each hour of additional molding time, and how many hours of molding time should they obtain at that price?

- Please include all details and steps performed to find your answers.