An automobile manufacturing company assembles two models of midsized and luxury cars in its plant in the South Industrial Park. The first model, the Thriller GL, is a four-door sedan with standard features, and excellent gas mileage. It is marketed as a smart buy for middle-class families with tight budgets. Each Thriller GL sold generates a modest profit of P180,000 for the company. The second model, the Cruiser LX, is a two-door luxury sedan with custom features, and navigational capabilities. It is marketed as a privilege of affluence for upper-middle-class families. Each Cruiser LX sold generates a healthy profit of P270,000 for the company. Rachel Rosencrantz, the manager of the assembly plant, is currently deciding the production schedule for the next month. Specifically, he must decide how many Thriller GLs and how many Cruiser LXs to assemble in the plant to maximize profit for the company. He knows that the plant possesses a capacity of 48,000 labor-hours during the month. He also knows that it takes six labor-hours to assemble one Thriller GL and 10.5 labor-hours to assemble one Cruiser LX. Because the plant is simply an assembly plant, the parts required to assemble the two models are not produced at the plant. Instead, they are shipped from other plants and suppliers to the assembly plant. For example, tires, steering wheels, windows, seals, and doors arrive from various supplier plants. For the next month, Rachel Rosencrantz knows that he will only be able to obtain 20,000 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 Thriller GL and the Cruiser LX use the same door parts, with four needed for the Thriller GL and two for the Cruiser LX. In addition, a recent company forecast of the monthly demands for the different automobile models suggests that the demand for the Cruiser LX is limited to 3,500 cars. There is no limit on the demand for the Thriller GL within the capacity limits of the assembly plant. a. Formulate and solve a linear programming model to determine the number of Thriller GLs and the number of Cruiser LXs that should be assembled next month. What is the optimal profit? b. What constraints limit profit? c. Should Rachel Rosencrantz consider increasing the capacity of the assembly plant? Why? d. Should Rachel Rosencrantz consider looking for additional suppliers of the doors? Why? e. Should General Ford's marketing department be urged to promote the models more aggressively in order to increase market demand? Why? Before he makes the final production decisions, Rachel Rosencrantz plans to explore the following questions independently, except where otherwise indicated. f. The marketing department knows that it can pursue a targeted P25,000,000 advertising campaign that will raise the demand for the Cruiser LX next month by 20 percent. Should the campaign be undertaken? g. Rachel Rosencrantz knows that he can increase next month's plant capacity by 25 percent by using overtime labor. With the new assembly plant capacity, how many Thriller GLs and how many Cruiser LXs should be assembled? h. Rachel Rosencrantz knows that overtime labor does not come without an extra cost. What is the maximum amount he should be willing to pay for all overtime labor beyond the cost of labor at regular-time rates. Express your answer as a lump sum. i. Rachel Rosencrantz explores the option of using both targeted advertising campaign and the overtime labor-hours. The advertising campaign raises the demand for the Cruiser LX by 20 percent, and the overtime labor increases the plant's labor-hour capacity by 25 percent. How many Thriller GLs and how many Cruiser LXs should be assembled using the advertising campaign and overtime labor-hours if the profit from each Cruiser LX sold continues to be 50 percent more than each Thriller GL sold? j Knowing that the advertising campaign costs P25,000,000 and the maximum usage of ovetime labor-nours costs P80,000,000 beyond regular time rates, is the solution found in part i a wise decision compared to the solution in part a ? k. Taking into consideration the requirements described in parts fj, what should be Rachel Rosencrantz's decisons on whether to undertake the advertising campaign, whether to use overtime labor, the number of Thriller GLs to assemble, and the number of Cruiser LXs to assemble? Explain your