The management of the Bovill Mukluk Factory (BMF) has decided to expand its prod
ID: 3253875 • Letter: T
Question
The management of the Bovill Mukluk Factory (BMF) has decided to expand its product mix. Market research studies have focused on diversifying the product line. BMF has decided to produce two lines of laptop computer cases: X-gens & Yeepies. Production is simple - cutting & sewing only. Assume this is a one day plan and they can sell all that are produced during the day. Contribution to profit is $30 per case for X-gens and $80 for Yeepies.
Production Constraints: Cutting Sewing
X-gens 3 hrs/case 2 hrs/case
Yeepies 2 hrs/case 4 hrs/case
The cutting line can run 1 1/2 shifts per day and the sewing line 2 shifts per day (assume 8 hr per shift).
Management Constraint: The boss’s son who unfortunately attended Bovill State University has just been placed in charge of supervising the Yeepie product line. Despite the BSU degree of your boss, you, as chief analyst, decide to require the production of at least two X-gens cases per day. BMF wants to know the number of X-gens and Yeepies to produce in order to maximize its total profit.
How many of what should we produce per day to maximize profit?
Explanation / Answer
Let X gens and Yeepies produced daily be x and y.
We need to maximize profit, i.e. Z = 30x+80y
Cutting line runs for 1.5 shits, i.e. 8*1.5=12 hours a day
Sewing line runs for 2 shifts, i.e. 8*2 = 16 hours a day
Total time spent on cutting = 3x+2y.
Hence, 3x+2y<=12
Total time spent on sewing = 2x+4y.
Hence, 2x+4y<=16
For non-negativity constraint we have : x,y>=0
COnstraint for production of at least 2 X-gens [er day : x>=2
Hence solving this we get : x=2, y=3 and Profit = 2*30+3*80 = $300
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