M limited as a result of past experience and estimates for the future, has decided that the cost of production of their sole product p an advanced process machine, is:

C=1064 +5X +0.04X2  

Where C=Total cost in Sh. 000

X=quantity produced and sold

The marketing has estimated that the price of the product is related to the quantity produced and sold by the equation.

P=157 -3X

Where P=price per unit in Sh. 000

X=quantity sold.

The government has proposed tax of Sh.t,000 per unit produced of P, but it is not expected that this will have any effect on the costs incurred in making P or on the demand/price relationship.

REQUIRED:

a). Determine the price and quantity that will maximize profit when there was no tax.

b). Determine the price and quantity that will maximize profit if the proposed tax is introduced.

c). The effect on the profit of the company if it was fixed at Sh.4000 per unit.