Reconsider the newspaper problem of Exercise, but now look at the news- paper's 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) Find the editorial and sales budget figures that maximize profit. Assume that the subscription price remains at $1.50/week, and the advertising price stays at $250/page. Use the five-step method, and model as a constrained optimization problem. Solve using the method of Lagrange multipliers. ?
(b) Calculate the shadow price for each constraint, and interpret their meaning. ?
(c) Draw a graph of the feasible region for this problem. Indicate the location of the optimal solution on this graph. Which of the constraints are binding at the optimal solution? How is this related to the shadow prices? ?
(d) Suppose that cuts in the editorial budget produce an unusually strong negative response in this market. Assume that a 10% cut in the editorial budget causes the paper to lose p% of its advertising and 2p% of its subscribers. Determine the smallest value of p for which the paper would be better off not to cut the editorial budget.
This is Exercise
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.