Mitchel\'s Machine Shop makes deluxe and regular skis on a weekly schedule for t
ID: 3050647 • Letter: M
Question
Mitchel's Machine Shop makes deluxe and regular skis on a weekly schedule for the area skiing enthusiasts. They also supply both regular and deluxe skis to local sporting goods stores.
A deluxe pair of skis requires 40 minutes for roughing and 20 minutes for finishing, whereas a regular pair of skis requires 20 minutes for roughing and 27 minutes for finishing. With only 1,000 minutes for roughing and 800 minutes of finishing time available per week and a profit realization of $4 and $3 for the deluxe and regular, respectively, what weekly mix of the two types of skis should be produced to meet the contract’s requirement and maximize profits.
Explanation / Answer
Maximum minutes available:
r = 1000
f = 800 f
Time to run each type of ski is:
Deluxe = 40r + 20f, where r is minutes of roughing and f is minutes of finishing
Regular = 20r + 27f
The profitability rate for each ski is 4 Euros/60 min and 3 Euros/47 minutes. This corresponds to 0.067 and 0.064 Euros per minute for the Deluxe and Regular skis, respectively. The Deluxe ski is slightly more profitable.
Profitability per minute can be stated as:
P=(4/60)D + (3/47)R = D/15 + (3/47)R
You must meet a minimum requirement of 18 regular skis.
18=R means that r=360, f=486 used
When R=18 you have 640 max and 314 max of r and f minutes left. These are your boundary conditions.
15 deluxe skis use up 600 r minutes and 300 f minutes.
This means you have 40 r and 14 f minutes left. No more skis can be made.
You will have 18 regular and 15 deluxe skis. This gives you a profitability of
P= (15 x 4) + (18 x 3)
= 114 Euros per week.
Per minute of actual process time, you have: 2.15