For digital photography fanatics, Dell sells high-end color scanners (S) and color printers (P).

There are 10,000 potential buyers per month, each interested in one unit of each product.

Potential buyers are differentiated with respect to their reservation prices (RP) for each of the

two products that have been estimated to range uniformly between $0 and $500 and to be

independent of each other.

1) What is the pair of prices that would maximize Dell's monthly revenue from these two

products?

d(p)=10,000-20p

r(p)=p*(10,000-20p)

2) Would Dell gain if they would sell these two products only as a bundle? What would be

the optimal price of the bundle?

d(p)=10,000*(1-p^2/500,000) for p<=500

d(p)=10,000*(1000-p)^2

/500,000 for p>=500

r(p)=p*d(p)

3) Suppose that Dell selects to give anyone buying a scanner a discount coupon of $50

towards the purchase of a printer. Would that promotion scheme be beneficial?

max revenue(Pp,Ps,C)=

10,000*[Pp*(prob(P))+Ps*(prob(S))+Pp+Ps-C*(prob(both))]

here C=50$

Give an

intuitive explanation.