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Finding the Optimal Number of Advertising Hours

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Problem: "Optimal Input Level."

Ticket Services, Inc., promotes concerts and sporting events. The college uses a team of ten students to hand deliver flyers at the mall, where every hour increment of flyer advertising costs $130. Over the past year, the following relation between advertising and ticket sales per event has been observed:
Sales (units) = 7,000 + 200A - 0.6A2 and ∆Sales/∆A = 200 - 1.2A

Here A represents one hour of flyer distribution and sales are measured in numbers of tickets.
Joe Smith, a senior student and team-leader has been asked to suggest an appropriate level of advertising. In thinking about this problem, Joe noted its resemblance to the optimal resource employment problem he had studied in a Managerial Economics course. The advertising-sales relation could be thought of as a production function with advertising as an input and sales as the output. The problem is to find the level of advertising that maximizes sales. After consultation with faculty in the Business Department, he determines that the value of output is $2 per ticket, the net marginal revenue earned (price minus all marginal costs except flyer advertising).

A. Continuing with Smith's production analogy, what is the marginal product of advertising?
B. Using the rule for optimal resource employment, determines the profit-maximizing number of flyer distribution hours.

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This solution depicts the required steps needed to find the optimal number of advertising hours in the given case.

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A. Continuing with Smith's production analogy, what is the marginal product of advertising?
Marginal product of ...

Solution provided by:
Lokesh Jain, MSc
Education
  • BEng (Hons) , Birla Institute of Technology and Science, India
  • MSc (Hons) , Birla Institute of Technology and Science, India
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