Linear Programming Applications Print the following pages and answer all questions on them Expedition Outfitters is a small company that manufactures speciality clothing for hiking, skiing, and mountain climbing. Company management has decided to begin production on two new parkas designed for use in extremely cold weather; the names selected for the two models are the Mount Everest Parka and the Rocky Mountain Parka. The company would like to schedule the production of each of the two models for the next three months. The manufacturing plant has 120 hours of cutting time and 120 hours of sewing time available for producing these two parkas each month. Each Mount Everest Parka requires 30 minutes of cutting time and 40 minutes of sewing time, and each Rocky Mountain Parka requires 20 minutes of cutting time and 26 minutes of sewing time. Additionally, management can decide to increase the total production time working on overtime. Each month 30 hours of cutting time and 30 hours of sewing time can be scheduled. The labour and material cost of the units produced on regular time is $140 for each Mount Everest and $50 for each RMP, while the units produced on overtime cost $160 and $65 respectively. The retail prices through the firms mail-order catalogue are $250 for the MEP and $200 for the RMP. Expedition outfitters own a storehouse where it can keep units in storage. There is enough space to store any amount of coats and it costs $3 to store one coat for a month, regardless of the model. Management would like to keep at least 50 units of each model in stock at the end of the quarter. Assuming that Expedition Outfitters has estimated the following demands for the next three months:

(a) Develop a linear model to determine the amount of coats that should be produced and stored each month in order to maximize the overall profit for the first quarter of the year.

(b) Develop an EXCEL spreadsheet to find the optimal solution for Expedition Outfitters. Make sure that your solution makes sense! (Submit the Excel file in Bb).

(c) Write a short report explaining what the best strategy for the company is.

(d) Due to some increase in raw material prices, the cost of producing each Mount Everest coat in March will increase by $5. Will this change the optimal production plan? And the total profit?

(e) Because of some improvements in the storage process, the cost of storing one coat can be reduced to $2.7. Can we determine using only the sensitivity analysis, what the new production plan would be? And the overall profit? If it is not possible, change this figure in the Excel and recalculate the solution. Report here the answer.

(f) If the sewing capacity could be increased in any of the three months, which would be the best month to assign some extra time to? Why?

Type of coat Mount Everest Rocky Mountain January February March 100 120 150 80 100 130 Type of coat Mount Everest Rocky Mountain January February March 100 120 150 80 100 130