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 pro?t 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 a|uminum- 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 pro?t.
a. Describe the analogy between this problem and the Wyndor Glass Co. problem discussed in Section 2.1. Then construct and ?ll in 8 table like Table 2.1 f0l' this problem, identifying b0th the 8CtiVltl€S and "18 |'8SOUI'C8S.
b.ldentify 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 target cell. Also show the Excel equation for each output cell expressed as a SUMPRODUCT fUnCtiOn. Then use the Excel Solver t0 solve thiS model.
e.lndicate why this spreadsheet model is a linear programming model.
f.Formulate this same model algebraically.
g.ldentify the decision variables, objective function, nonnegativity constraints, functional constraints, and parameters in both the algebraic version and spreadsheet version of the m0d8l-
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 thecompany 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 considenng 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 6 wood frames per day?