oes Coffee Shoppe has fresh doughnuts delivered each morning

oe\'s Coffee Shoppe has fresh doughnuts delivered each morning. Daily demand for plain doughnuts is approximately normal with a mean of 200 and a standard deviation of 30. Joe pays $0.20 per doughnut and sells it for $0.55. At the end of the day, 2/3 of the unsold doughnuts are sold at 0.25 each, and Joe and the staff eat any leftovers. Which of the following ranges includes the optimal order size?

Need step by step instructions please.

Solution

Joe pays per doughnut= 0.20

Sells at                        = 0.55

Hence gain per doughnut =0.35

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2/3 of nuts give gain per doughnut = 0.05

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Daily demand = 200

std dev = 30

Construct confidence interval for 95%

(200-1.96(30), 200+1.96(30))

= (141.2, 258.8)

For the lowest 141.2 demand, profit will be calculated as

141.2(0.35) =49.42

For the highest 258.8 demand , profit is

200(0.35) + 58.8(2/3)(0.05) = 70+1.96=71.96

Hence optimal order size = 258.8