MAGANGA Co$.$ Ltd has a factory capacity of $1,200$ units per month. Units cost him Tsh $\frac{60}{?}=$ to make and its normal selling price is Tsh $110/=$ each. However the demand per month is uncertain and is as follows:

$\backslash$table$[[$Demand$,$Probability$],[400,0\mathrm{.}2],[500,0\mathrm{.}3],[700,0\mathrm{.}4],[900,0\mathrm{.}1]]$

The company has been approached by a customer who is ready to contract a fixed quantity per month at a price of Tsh $90$ per unit. The customer is prepared to sign a contract to purchase $300,500,700$ or $800$ units per month. The company can vary production levels during the month up to the maximum capacity, but cannot carry forward any unsold units in its iriventory.

Required:

a$)$ Calculate all possible profits that could result

b$)$iExpected value

ii$)$Maximin

iii$)$Maximax

iv$)$Minimax regret

c$)$What is the most that the company would be prepared to pay in order to obtain perfect knowledge as to the level of demand?