A local daily newspaper has recently been acquired by a large media conglomerate. The paper currently sells for $1.50/week and has a circulationof...

A local daily newspaper has recently been acquired by a large media conglomerate. The paper currently sells for $1.50/week and has a circulationof 80,000 subscribers. Advertising sells for $250/page, and the papercurrently sells 350 pages/week (50 pages/day). The new management islooking for ways to increase profits. It is estimated that an increase of ten cents/week in the subscription price will cause a drop in circulationof 5,000 subscribers. Increasing the price of advertising by $100/page willcause the paper to lose approximately 50 pages of advertising per week.The loss of advertising will also affect circulation, since one of the reasonspeople buy the paper is for the advertisements. It is estimated that a lossof 50 pages of advertisements per week will reduce circulation by 1,000subscriptions.

 Reconsider the newspaper problem of Exercise 7, but now suppose thatadvertisers have the option of using direct mail to reach their customers.Because of this, management has decided not to increase the price ofadvertising beyond $400/page

 Find the weekly subscription price and the advertising price that

will maximize profit. Use the five-step method, and model as a constrained

optimization problem. Solve by the method of Lagrange

multipliers.