Automobile alliance, a large automobile manufacturing company, organizes the vehicles it manufactures into three families: a family of trucks, a family of small cars and a family of midsized and luxury cars. One plant outside Detroit, MI assembles two models from the family of midsized and luxury cars .The first model, the family thrill seeker, is a four-door sedan with vinyl seats, plastic interior, standard features, and excellent gas mileage .It is marked as as a smart buy for middle -class families with tight budgets, and each family thrill seeker sold generates a modest profit of $3,600 for the company. The second model, the classy cruiser, is a two -door luxury sedan with leather seats, wooden interior, custom features, and navigational capabilities. It is marked as a privilege of affluence for upper-middle -class families, and each classy cruiser sold generates a health profit of $5,400 for the company. Rachel Rosencrantz, the manager of assembly plant, is currently deciding the production schedule for the next month. Specifically, she must decide how much family.

Thrill seekers and how many classy cruisers to assemble in the plant to maximize profit for the company. She knows that the plant possesses a capacity of 48,000laborhours during the month she also knows that it takes 6 labor-hours to assemble one family thrill seeker and 10.5 labor-hours to assemble one classy cruiser. Because the plant is simply an assembly plant, the part required to assemble the two models are not produced at the plant. They are instead shipped from other plant around the Michigan area to the assembly plant. For example, tires, steering wheels, windows, seat and doors all arrive from various supplier plants. For the next month, Rachel knows that she will be able to obtain only 20,000 doors (10,000 left -hand doors and 10,000 right-hand doors) from the door supplier. A recent labor strike forced the shutdown of that particular supplier plant for several days, and that plant will not be able to meet its production schedule for the next month. Both the family thrill seeker and the classy cruiser use the same door part

In addition, a recent company forecast of the monthly demands for different automobile model s suggests that the demand for the classy cruiser is limited to 3,500 cars. There is no limit on the demand for the family thrill seeker within the capacity limits of the assembly plant

(a) Formulate and solve a linear programming problem/model to determine the number of family thrill seekers and the number of classy cruisers that should be assembled just using graphical or simplex method.

Before she makes her final production decisions, Rachel plants to explore the following questions independently except where otherwise indicated.

(b) 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?

(c) 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 thrill seekers and how many classy cruisers should be assembled?

(d) Rachel knows that over time 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.

(e) 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 thrill seekers and how may classy cruisers should be assembled using the advertising campaign campaign and overtime labor-hours if the profit from each classy cruiser sold continues to be 50percent more than for each family thrill seeker sold ?

(f) Knowing that the advertising campaign costs $500,000 and the maximum usage of overtime labor-hour cost $1,6000,000 beyond regular time rates, is the solution found in part (e) a wise decision compared to the solution found in part (a)

(g) Automobile alliance has determined that dealerships are actually heavily discounting the price of the family thrill seekers 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 thrill seekers and the number of classy cruisers that should be assembled given this new discounted price.

(h) The company has discovered quality problems with the family thrill seeker by randomly testing thrill seekers at the end of the assembly line .inspectors discovered that in over 60 percent of the cases, two of the four doors on s thrill seeker do not seal properly. Because the percentage of defective thrill seekers determined by the random testing is so high, the floor supervisor has decided to perform quality control tests on every thrill seeker at the end of the line. Because of the added tests, the time it takes to assemble one family. thrill seeker has increased from 6to 7.5 hours. Determine the number of units of each model that should be assembled given the new assembly time for the family thrill seeker.

(i) The board of directors of automobile alliance wishes to capture 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 (a). they then ask her to meet the full demand for classy cruisers if the decrease in profit is not more than $20,000,000

(j) Rachel now makes her final decision by combining all the new considerations described in part (f), (g), and (h). What is her final decision on whether to undertake the advertising campaign, whether to use overtime labor, the number of family thrill seekers to assemble, and the number of classy cruisers to assemble?