MUST SHOW YOUR WORK LEADING TO YOUR ANSWERS IN ORDER TO RECEIVE FULL CREDIT FOR THE QUESTION: 6….

MUST SHOW YOUR WORK LEADING TO YOUR ANSWERS IN ORDER TO RECEIVE FULL CREDIT FOR THE QUESTION: 6. The manager of a retail store has just been fired for setting prices too low (he didn’t understandthe concept of Mark-up % and in order to price the items at 60% Mark-up, he had been adding60% to the cost of each item). He has since taken Halimi’s class and now knows exactly how toprice merchandise.He is considering opening his own retail store and has begun an analysis of the market. There aretwo possible sites that he is considering. If he opens his store at Site 1 and demand is high, he willgenerate an annual profit of $50,000. If demand is low, he will lose $10,000 per year. If he openshis store at Site 2 and demand is high, he will generate an annual profit of $80,000, but ifdemand is low, he will lose $30,000 per year. He believes that there is a 60% chance that demandwill be high.a. Assuming he wants to maximize profit, which location should he choose?b. Which location should he choose if he wants to maximize his utility, assuming the followingutilities for each profit/loss?U($80,000) = 1,U($50,000) = 0.72,U($-10,000) = 0.22,U($-30,000) = 0
Work and calculations
a. Expected profit (maximize profit)
Probability demand high = 0.60; probability demand low = 0.40
Site 1 outcomes: +$50,000 (high), −$10,000 (low)
Expected profit for Site 1:
EV1 = 0.60 × 50,000 + 0.40 × (−10,000)
EV1 = 30,000 − 4,000
EV1 = $26,000
Site 2 outcomes: +$80,000 (high), −$30,000 (low)
Expected profit for Site 2:
EV2 = 0.60 × 80,000 + 0.40 × (−30,000)
EV2 = 48,000 − 12,000
EV2 = $36,000
Comparison: EV2 ($36,000) > EV1 ($26,000) → choose Site 2 to maximize expected profit.
b. Expected utility (maximize utility)
Given utilities:
U($80,000) = 1
U($50,000) = 0.72
U($-10,000) = 0.22
U($-30,000) = 0
Expected utility for Site 1:
EU1 = 0.60 × U($50,000) + 0.40 × U($-10,000)
EU1 = 0.60 × 0.72 + 0.40 × 0.22
EU1 = 0.432 + 0.088
EU1 = 0.520
Expected utility for Site 2:
EU2 = 0.60 × U($80,000) + 0.40 × U($-30,000)
EU2 = 0.60 × 1 + 0.40 × 0
EU2 = 0.60
Comparison: EU2 (0.60) > EU1 (0.520) → choose Site 2 to maximize expected utility.
Final answers
a. Choose Site 2 to maximize expected profit (EV2 = $36,000 > EV1 = $26,000).
b. Choose Site 2 to maximize expected utility (EU2 = 0.60 > EU1 = 0.520).