Question a is important. If someone just does question a that will be okay. But a must be done as a function of x1 and x2 only. Reconsider the newspaper problem of Exercise7, but now look at the news- papers business expenses. The current weekly business expenses for the paper are as follows: $80,000 for the editorial department (news, features, editorials); $30,000 for the sales department (advertising); $30,000 for the circulation department; and $60,000 in fixed costs (mortgage, utilities, maintenance). The new management is considering cuts in the editorial department. It is estimated that the paper can operate with a minimum of a $40,000/week editorial budget. Reducing the editorial budget will save money, but it will also affect the quality of the paper. Experience in other markets suggests that the paper will lose 2% of its subscribers and 1% of its advertisers for every 10% cut in the editorial budget. Management is also considering an increase in the sales budget. Recently the management of another paper in a similar market expanded its advertising sales budget by 20%. The result was a 15% increase in advertisements. The sales budget may be increased to as much as $50,000/week, but the over- all budget for business expenses will not be increased beyond the current level of $200,000/week. (a) Based on the description of the problem, write a formula for the profit function f(x1; x2), where x1 is the weekly editorial expense and x2 is the weekly sales budget. Write the constraint set S for x1, x2. (b) Assuming that the function f(x1; x2) from question (a) is linear, give a precise description of a finite set of points on which the maximum of f over S is attained. Hint. Non-constant linear functions do not have critical points. (c) Find the maximum point and the maximum value of f over S. (d) What is your verbal recommendation to the editorial board of the newspaper? What would be the best way to proceed to maximize profit? (e) Calculate the shadow price for each constraint and interpret their meaning. This is Exercise #7 A local daily newspaper has recently been acquired by a large media con- glomerate. The paper currently sells for $1.50/week and has a circulation of 80,000 subscribers. Advertising sells for $250/page, and the paper currently sells 350 pages/week (50 pages/day). The new management is looking for ways to increase profits. It is estimated that an increase of ten cents/week in the subscription price will cause a drop in circulation of 5,000 subscribers. Increasing the price of advertising by $100/page will cause the paper to lose approximately 50 pages of advertising per week. The loss of advertising will also affect circulation, since one of the reasons people buy the paper is for the advertisements. It is estimated that a loss of 50 pages of advertisements per week will reduce circulation by 1,000 subscriptions.