Famous Albert pride himself on being the Cookie King of the? West.? Small, freshly baked cookies are the specialty of the shop. Famous Albert has asked for help to determine the number of cookies he should make each day. From an analysis of the past demand he estimates demand for? cookies? as:
?Demand? (dozens) Probability of demand
??1,800 0.05
??2,000 0.10
??2,200 0.20
??2,400 0.30
??2,600 0.20
??2,800 0.10
??3,000 0.05
Each dozen sells? for? $0.69 and? costs? $0,49, which includes handling and transportation. Cookies that are not sold at the end of the day are reduced? to? $.29 and sold the following day? as? day-old merchandise.
??a) What is the optimal number of cookies? to? make?
??b) What is the maximum? expected? profit?
a) Optimal number is the sum of all the demand variables multiplied with their probabilities.
Optimal number of cookies = (1800*0.05) +( 2000*0.1) + (2200*0.2) + (2400*0.3) + (2600*0.2) +(2800*0.1) + (3000*0.05)
= 2400 is the optimal number to make corresponding to respective demands
b) maximum expected profit is thinking that every cookie gets sold on the same day itself
making price = 0.49$
selling price = 0.69$
profit = 0.2$
Expected profit = Expected demand * expected profit per cookie
= 0.2 * 2400
= $480
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