Ali Jones produces two types of cowboy hats. A type 1 hat requires twice as much labor time as type 2. If all the available labor time is dedicated to type 2 alone, the company can produce a total of 400 type 2 hats a day. The respective market limits for the two types are 150 and 200 hats per day. The revenue is P8 per type 1 hat and P5 per type 2 hat. a. Formulate an LP model and use the graphical solution to determine the number of hats of each type that maximizes revenue b. Determine the dual price of the production capacity (in terms of the type 2 hat) and the range for which it is applicable c. If the daily demand limit on type 1 hat is decreased to 120, use the dual price to determine the corresponding effect on the optimal revenue d. What is the dual price of the market share of the type 2 hat? By how much can the market share be increased while yielding the computed worth per unit?

Ali Jones produces two types of cowboy hats. A type 1 hat requires twice as much labor time as type 2. If all the available labor time is dedicated to type 2 alone, the company can produce a total of 400 type 2 hats a day. The respective market limits for the two types are 150 and 200 hats per day. The revenue is P8 per type 1 hat and P5 per type 2 hat. a. Formulate an LP model and use the graphical solution to determine the number of hats of each type that maximizes revenue b. Determine the dual price of the production capacity (in terms of the type 2 hat) and the range for which it is applicable c. If the daily demand limit on type 1 hat is decreased to 120, use the dual price to determine the corresponding effect on the optimal revenue d. What is the dual price of the market share of the type 2 hat? By how much can the market share be increased while yielding the computed worth per unit?

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter6: Optimization Models With Integer Variables

Section6.4: Fixed-cost Models

Problem 15P

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