A manufacturer of tablet computers currently sells 10,000 units per month of a basic model. The...
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A manufacturer of tablet computers currently sells 10,000 units per month of a basic model. The cost of manufacture is $700/unit and the wholesale price is $950. During the last quarter the manufacturer lowered the price $100 in a few test markets, and the result was a 50% increase in sales we will call this the price elasticity. The company has been advertising its products nationwide at a cost of $50,000 per month. The advertising agency claims that increasing the advertising budget by $5,000/month would result in a sales increase of 100 units/month. Management has agreed to consider an increase in the advertising budget to no more than $75,000/month. a) Determine the price and the advertising budget that will maximize profit. Use the five-step method. Model as a constrained optimization problem, and solve using the method of Lagrange multipliers. b) Determine the sensitivity of the decision variables (price and advertis- ing) to price elasticity. c) Determine the sensitivity of the decision variables to the advertising agency's estimate of 100 new sales cach time the advertising budget is increased by $5,000/month. d) What is the value of the multiplier found in part (a) i.e. the first bulleted item above? What is the real world significance of the multiplier? How could you use this information to convince top management to lift the ceiling on advertising expenditures? Notes: 5000 8- 10000+ (950-p) + (a-50000) 100 where the factor 5000 is called the the price elasticity and where we assume the following notation • p= price ($/computer), s sales (computers/month), a= advertising budget ($/month). A manufacturer of tablet computers currently sells 10,000 units per month of a basic model. The cost of manufacture is $700/unit and the wholesale price is $950. During the last quarter the manufacturer lowered the price $100 in a few test markets, and the result was a 50% increase in sales we will call this the price elasticity. The company has been advertising its products nationwide at a cost of $50,000 per month. The advertising agency claims that increasing the advertising budget by $5,000/month would result in a sales increase of 100 units/month. Management has agreed to consider an increase in the advertising budget to no more than $75,000/month. a) Determine the price and the advertising budget that will maximize profit. Use the five-step method. Model as a constrained optimization problem, and solve using the method of Lagrange multipliers. b) Determine the sensitivity of the decision variables (price and advertis- ing) to price elasticity. c) Determine the sensitivity of the decision variables to the advertising agency's estimate of 100 new sales cach time the advertising budget is increased by $5,000/month. d) What is the value of the multiplier found in part (a) i.e. the first bulleted item above? What is the real world significance of the multiplier? How could you use this information to convince top management to lift the ceiling on advertising expenditures? Notes: 5000 8- 10000+ (950-p) + (a-50000) 100 where the factor 5000 is called the the price elasticity and where we assume the following notation • p= price ($/computer), s sales (computers/month), a= advertising budget ($/month).
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Related Book For
Advanced Accounting
ISBN: 978-1305084858
12th edition
Authors: Paul M. Fischer, William J. Tayler, Rita H. Cheng
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