Precision Castings Incorporated has received an order for precision castings. Th

Question

Precision Castings Incorporated has received an order for precision castings. The cost of producing each casting is estimated to be $2000. The customer agrees to pay a total of $15,000 for three good castings, a total of $18,000 for four good castings, and a total of $20,000 for five good castings. If fewer than three good castings are produced, none will be purchased; good castings in excess of five will not be purchased. If fewer than three good castings are available, a shortage cost of $10,000 in excess of the cost of production will be incurred regardless of the number short. Each casting is produced independently; the probability of an individual casting being acceptable is believed to be 0.70

(a) Develop the expected profit to me maximized

(b) Determine the number of units to schedule to maximize expected profit (hint: the number is greater than 4)

(c) If five castings are produced, what is the probability that the firm will lose money?

Explanation / Answer

the probability of an individual casting being acceptable = 0.70

total castings made= N

Cost of N castings = 2000*N

If N = 3, then total casting being acceptable = 0.7*3=2.1. it will not be sold.

We want total casting being acceptable should be between 3 to 5. then only profit will happen.

For that Total casting that should be attempted be = 3/0.7 = 4.28 to 5/0.7 = 7.14

OR from 5 to 8 castings be made for profit

B. for profit maximization

if 3 castings are sold, then total castings scheduled should be 3/0.7 or 5 should be attempted

   Profit = 15000( for 3 castings) -5*2000 =5000

   if 4 are sold then 4/0.7 = 5.71 or 6

     Profit = 18000( for 4 castings) - 6*2000 = 6000

profit price of 5 castings = 20000 - 8*2000 = 4000

so for maximum profit 6 castings should be scheduled and total profit expected be 4000

(c) if five are produced then firm will lose money if fewer than 3 complete castings are made. probabilty is

30 % that firm will lose money

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