Question

A computer & accessories retailer has purchased three projectors of a certain type at Rs.50000 per projector. He will sell them for Rs. 100,000 per projector. The manufacturer has agreed to repurchase any projectors still unsold after a specified period at Rs. 20, 000 per projector. Suppose that the chances for the number of projectors sold are p(0) =0.4, p(1) =0.2, p(2) =0.3 and p(3) =0.1 respectively. Find the expected profit for the retailer.

Answer 1

Let, X= no of projectors sold.

The possible values of x are 0,1,2,3

the pmf of x is given as-

x	0	1	2	3
p(x)	0.4	0.2	0.3	0.1

let U(x) be the profit from selling x units

then U(x)= revenue- cost of purchase

Here, revenue is obtained by adding the amount of selling x projectors at a price of 100000 to a customer and selling (3-x) projectors at a price of 20000 to the manufactirer

hence, revenue= 100000*x+(3-x)*20000

and cost of purchasing 3 projectors= 3*50000= 150000

then, U(x)=100000*x+(3-x)*20000-150000 = 80000*x-90000

Then, expected profit= E[U(x)]= U(0)*p(0) + U(1)*p(1) + U(2)*p(2) + U(3)*p(3)

= (-90000)*0.4 + (-10000)*0.2 + 70000*0.3 + 150000*0.1

= -36000-2000+21000+15000 = -2000

Hence, the retailer has an expected profit of Rs (-2000), i.e., he has a loss of 2000