1. 1. A company has determined that the relationship between the sales price for
ID: 1130449 • Letter: 1
Question
1. 1. A company has determined that the relationship between the sales price for one of its products and the quantity sold per week is P - 650- 10D per unit, where D is the demand or quantity sold per week and p is the price in dollars). Fixed weekly costs are $1000, and the variable cost is $25/unit. (20 pts) What number of units should be produced per week and sold to maximize net profit? a) (10 pts) b) What is the maximum profit per week associated with this product? (5 pts) c) What is the breakeven points? (10 pts)Explanation / Answer
a) Profit = Total revenue - Total cost
Total revenue (TR) = P x D = 650D - 10D2
Total cost (TC) = 1000 + 25D
Profit would be maximized where MR = MC:
MR = d(TR)/dD = 650 - 20D
MC = d(TC)/dD = 25
D = 31.25
P = 337.5
b) Profit = 337.5 x 31.25 - 1000 - 25 x 31.25 = $ 8765.625
c) Break even point: Profit = 0
650D - 10D2 - (1000 + 25D) = 0
D = 1.643 or D = 60.857
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