Harriet is trying to determine how many units of two types of lawn mowers to produce each day. One of these is the Standard model, while the other is the Deluxe model. The profit per unit on the Standard model is $60, while the profit per unit on the Deluxe model is $40. The Standard model requires 20 minutes of assembly time, while the Deluxe model requires 35 minutes of assembly time. The Standard model requires 10 minutes of inspection time, while the Deluxe model requires 15 minutes of inspection time. The company must fill an order for 6 Deluxe models. There are 450 minutes of assembly time and 180 minutes of inspection time available each day. How many units of each product should be manufactured to maximize profits?
Show all of your work and provide evidence that you can set up and solve a linear programming (LP) problem. Clearly identify your answer(s) and provide a brief discussion of the results. You may use the POM (preferred and easier) software or another software to complete this problem. Submit your results from the software in an Excel file and answer each of the questions below in that file.
QUESTIONS:
a. Formulate and solve the problem as a linear programming problem
b. Are the two resources (assembly time and inspection time) fully used? If so, which one(s)?
c. If a resource is not fully used, how much of it is unused?
d. Over what range of prices for the Standard model would the solution you obtained remain the same. To answer this question you could use the ranging window in POM.
e. If you could obtain one more unit of the assembly time or inspection time how much would you be willing to pay for that additional resource?