Ruth Jones, the marketing manager for a department store chain is  trying to decide on the optimal allocation of her advertising budget for the next quarter. Jones has the data that indicate that television commercials and newspaper advertisements have the following impact on sales revenue (R)\r\n

R = 20,000T + 5000N + 20,000TN - 1O00T2\r\n

where T represents the number of commercials on T.V. and N the number of full page newspaper advertisements. Each T.V. commercial costs $10,000 and each newspaper advertisement costs $5000. The advertising budget is limited to be $100,000.\r\n

(a) Calculate the optimal amount of advertisement in each medium if the firm is interested in maximizing its sales revenue. Calculate the consequent value of sales revenue.\r\n

(b )By how much should sales revenue increase if the advertising budget increases by a very small amount? Show and explain your calculations.\r\n
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