The buzz campus eatery offers a specific type of biscuits for $1.5 each from 8am

Question

The buzz campus eatery offers a specific type of biscuits for $1.5 each from 8am to 3pm. The biscuits are ordered from a supplier at the start of each day and delivered before the store opens. The supplier charges 75 cents per biscuit. If, at 3pm, some biscuits are left, the buzz people mark down the price and sell off all the remaining biscuits for 50 cents each. In contrast, if, before 3pm, a customer comes to buy a biscuit but buzz has run out of biscuits, the buzz gives a free coupon worth 10 cents to the customer as compensation. Demand for biscuits before 3pm at buzz is variable but can only be 40 to 45, with probabilities given in the following table.

Number of customers Probability
40 0.1
41 0.15
42 0.25
43 0.25
44 0.15
45 0.1

(e) How many biscuits should Oz order in order to maximize the expected profit?

Explanation / Answer

Biscuits Selling Price Total Sales Cost Profit before Cupone Cost Net Profit ($ 1.125) Each Free Cupone $0.15 each 40 1.5 60 45 15 6 9 41 1.5 61.5 46.125 15.375 6.15 9.225 42 1.5 63 47.25 15.75 6.3 9.45 43 1.5 64.5 48.375 16.125 6.45 9.675 44 1.5 66 49.5 16.5 6.6 9.9 45 1.5 67.5 50.625 16.875 6.75 10.125 If he sold 45 Biscuits he will get Profit of $10.125, there is only 10% probability to sell 45 Biscuits. But as per probability: =(40*0.1)+(41*0.15)+(42*0.25)+(43*0.25)+(44*0.15)+(45*0.1) = 42.5 customers will come. if he order 42 biscuts he can get Profit $9.45 if he order 43 biscuts he can get Profit of $9.675 Thank you..... = 42.5 customers will come. if he order 42 biscuts he can get Profit $9.45 if he order 43 biscuts he can get Profit of $9.675 Thank you..... Biscuits Selling Price Total Sales Cost Profit before Cupone Cost Net Profit ($ 1.125) Each Free Cupone $0.15 each 40 1.5 60 45 15 6 9 41 1.5 61.5 46.125 15.375 6.15 9.225 42 1.5 63 47.25 15.75 6.3 9.45 43 1.5 64.5 48.375 16.125 6.45 9.675 44 1.5 66 49.5 16.5 6.6 9.9 45 1.5 67.5 50.625 16.875 6.75 10.125

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