M3 Participation Activity
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Jun 8, 2024
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M3 Participation Activity:
Q1: Suppose Blue Ridge can order additional pumps from a third party for the production, what is maximum rate that Blue Ridge like to pay for each additional pump?
Blue Ridge will pay the shadow price ($200) for each additional pump up to 207 pumps. Q2: If Blue Ridge decides to purchase 10 pumps, what impact will this have on total profit and the optimal solution?
Our allowable increase is 7 meaning we at most can only order 207 pumps. If
we decide to purchase 10 it puts us out of the range of feasibility.
Q3: How much (at most) would you like to pay for 2 more pumps?
At most would be 200*2=$400 total
Q4: How much (at most) would you like to pay for 100 labor hours?
100*16.667=$1666.7
Q5: How much (at most) would you like to pay for 2 more pumps and 100 labor hours together?
100% Rule: (2/7)+(100/234)<100%
=200*2+16.667*100=2066.7
Q6: Suppose a new Hot Tub (the Typhoon-Lagoon) is being considered. It generates a marginal profit of $320
and requires:
1 pump (shadow price = $200)
8 hours of labor (shadow price = $16.67)
13 feet of tubing (shadow price = $0) Would it be profitable to produce any? 320-200*1-16.67*8-0*13=-13.33 < 0
Therefore it would not be profitable.
Q7: Suppose a Typhoon-Lagoon required only 7 labor hours rather than 8. Is it now profitable to produce any? 320-200*1-16.67*7-0*13=3.31>0
Yes, it would be profitable
Q8: What is the maximum amount of labor Typhoon-Lagoons could require and still be profitable?
320-200*1-16.67X3-0*13. >0
=120/16.67=7.20
7.20 hours is the max amount of labor to be profitable.
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