Theory + Problem on Inventory model 3 with probabilistic demand

Solve 1 problem on inventory model 3a with probabilistic demand for which instantaneous demand, set up cost zero, stock level discrete and lead time zero by using important formulas.

Solve problem on inventory model 3b with probabilistic demand for which instantaneous demand, no set up cost, stock level continuous and lead time zero by using important formulas.

A baking company sells one of its types of cake by weight. It makes a profit of 95 paise a pound on every pound of cake sold on the day it is baked. It disposes of all cakes, not sold on the day they are baked at a loss of 15 paise a pound. Of demand is known to have probability density function
f (R) = 0.03 - 0.0003 R
Find the optimum amount of cake the company should bake daily.

A fish stall sells a variety of fish at the rate of Rs 5 per kg on the day of catch. If the stall fails to sell the catch on the same day, it pays for storage at the rate of Rs 0.30 per kg and the price fetched is Rs 4.50 per kg on the next day. Past records show that there is an unlimited demand for fish one day old. The problem is to ascertain how much fish should be procured every day so that the total expected cost is minimum. It has been found from the past records that the daily demand follows an exponential distribution with
f (x) = 0.02 e^ -0 02 x
[Bombardier B. Sc stat. 1984, B. Sc. Appl. Comp. 1984]

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