The Whitt Window Company is a company with only three employees that makes two different kinds of handcrafted windows: a wood-framed and an aluminum framed window. They earn $60 profit for each wood-framed window and $30 profit for each aluminum-framed window. Doug makes the wood frames and can make 6 per day. Linda makes the aluminum frames and can make 4 per day. Bob forms and cuts the glass and can make 48 square feet of glass per day. Each wood-framed window uses 6 square feet of glass and each aluminum-framed window uses 8 square feet of glass.

The company wishes to determine how many windows of each type to produce per day to maximize total profit.

a. Describe the analogy between this problem and the Wyndor Glass Co. problem discussed in Section 2.1. Then construct and fill in a table like Table 2.1 for this problem, identifying both the activities and the resources.

TABLE 2.1: Data for the Wyndor Glass Co. Product-Mix Problem

b. Identify verbally the decisions to be made, the constraints on these decisions, and the overall measure of performance for the decisions.
c. Convert these verbal descriptions of the constraints and the measure of performance into quantitative expressions in terms of the data and decisions.
d. Formulate a spreadsheet model for this problem. Identify the data cells, the changing cells, and the objective cell. Also show the Excel equation for each output cell expressed as a SUMPRODUCT function. Then use Solver to solve this model.
e. Indicate why this spreadsheet model is a linear programming model.
f. Formulate this same model algebraically.
g. Identify the decision variables, objective function, non-negativity constraints, functional constraints, and parameters in both the algebraic version and spreadsheet version of the model.
h. Use the graphical method to solve this model.
i. A new competitor in town has started making wood-framed windows as well. This may force the company to lower the price it charges and so lower the profit made for each wood-framed window. How would the optimal solution change (if at all) if the profit per wood-framed window decreases from $60 to $40? From $60 to $20?
j. Doug is considering lowering his working hours, which would decrease the number of wood frames he makes per day. How would the optimal solution change if he only makes 5 wood frames per day?

Transcribed Image Text:

Production Time Used for Each Unit Produced Available per Week Plant Doors 1 hour Windows 4 hours 12 hours 2 hours 2 hours $500 18 hours 3 hours Unit profit $300