$3\mathrm{.}1-7.$ The Whitt Window Company is a company with only three

employees which makes two different kinds of hand$-$crafted windows: a wood$-$framed and an aluminum$-$framed window. They earn

$$180$ profit for each wood$-$framed window and $$90$ 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 Sec. $3\mathrm{.}1.$ Then construct and

fill in a table like Table $3\mathrm{.}1$ for this problem, identifying both

the activities and the resources.

$($b$)$ Formulate a linear programming model for this problem.

D$,$I $($c$)$ Use the graphical method to solve this model.

I $($d$)$ A new competitor in town has started making wood$-$framed

windows as well. This may force the company to lower the

price they charge and so lower the profit made for each woodframed window. How would the optimal solution change $($if at

all$)$ if the profit per wood$-$framed window decreases from $$180$

to $$120?$ From $$180$ to $$60?($You may find it helpful to use

the Graphical Analysis and Sensitivity Analysis procedure in

IOR Tutorial.$)$

I $($e$)$ 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 makes only $5$ wood

frames per day? $($You may find it helpful to use the Graphical

Analysis and Sensitivity Analysis procedure in IOR Tutorial.$)$

$3\mathrm{.}1-8.$ The WorldLight Company produces two light fixtures

$($products $1$ and $2)$ that require both metal frame parts and electric