$($a$)[5$ points$]$ Formulate this problem as a linear programming problem.

$($b$)[5$ points$]$ Using Excel Solver, solve for the optimal solution for this problem to determine

the number of Family Thrillseekers and the number of Classy Cruisers that should be

assembled.

Before she makes her final production decisions, Rachel plans to explore the following

questions independently except where otherwise indicated.

$($c$)[2\mathrm{.}5$ points$]$ The marketing department knows that it can pursue a targeted $$500,000$

advertising campaign that will raise the demand for the Classy Cruiser next month by $20$

percent. Should the campaign be undertaken?

$5$

$($d$)[5$ points$]$ Rachel knows that she can increase next month$$s plant capacity by using

overtime labor. She can increase the plant$$s labor hour capacity by $25$ percent. With the

new assembly plant capacity, how many Family Thrillseekers and how many Classy

Cruisers should be assembled?

$($e$)[2\mathrm{.}5$ points$]$ Rachel knows that overtime labor does not come without an extra cost. What

is the maximum amount she should be willing to pay for all overtime labor beyond the cost

of this labor at regular time rates? Express your answer as a lump sum.

$($f$)[5$ points$]$ Rachel explores the option of using both the targeted advertising campaign and

the overtime labor$-$hours. The advertising campaign raises the demand for the Classy

Cruiser by $20$ percent, and the overtime labor increases the plant$$s labor$-$hour capacity by

$25$ percent. How many Family Thrillseekers and how many Classy Cruisers should be

assembled using the advertising campaign and overtime labor$-$hours if the profit from each

Classy Cruiser sold continues to be $50$ percent more than for each Family Thrillseeker sold?

$($g$)[5$ points$]$ Knowing that the advertising campaign costs $$500,000$ and the maximum usage

of overtime labor$-$hours costs $$1,600,000$ beyond regular time rates, is the solution found

in part $($f$)$ a wise decision compared to the solution found in part $($b$)?$

$($h$)[5$ points$]$ Automobile Alliance has determined that dealerships are actually heavily

discounting the price of the Family Thrillseekers to move them off the lot. Because of a

profit$-$sharing agreement with its dealers, the company is therefore not making a profit of

$$3,600$ on the Family Thrillseeker but is instead making a profit of $$2,800.$ Determine the

number of Family Thrillseekers and the number of Classy Cruisers that should be

assembled given this new discounted price.

$($i$)[5$ points$]$ The company has discovered quality problems with the Family Thrillseeker by

randomly testing Thrillseekers at the end of the assembly line. Inspectors have discovered

that in over $60$ percent of the cases, two of the four doors on a Thrillseeker do not seal

properly. Because the percentage of defective Thrillseekers determined by the random

testing is so high, the floor supervisor has decided to perform quality control tests on every

Thrillseeker at the end of the line. Because of the added tests, the time it takes to assemble

one Family Thrillseeker has increased from $6$ to $7\mathrm{.}5$ hours. Determine the number of units

of each model that should be assembled given the new assembly time for the Family

Thrillseeker.

$($j$)[5$ points$]$ The board of directors of Automobile Alliance wishes to capture a larger share

of the luxury sedan market and therefore would like to meet the full demand for Classy

Cruisers. They ask Rachel to determine by how much the profit of her assembly plant

would decrease as compared to the profit found in part $($b$).$ They then ask her to meet the

full demand for Classy Cruisers if the decrease in profit is not more than $$2,000,000.$

$($k$)[5$ points$]$ Rachel now makes her final decision by combining all the new considerations

described in parts $($g$),($h$),$ and $($i$).$ What are her final decisions on whether to undertake the

advertising campaign, whether to use overtime labor, the number of Family Thrillseekers

to assemble, and the number of Classy Cruisers to assemble?