ABC is a small manufacturer of two types of popular all-terrain snow skis, the J and the D models. The manufacturing process consists of two principal departments: fabrication and finishing. The fabrication department has 12 skilled workers, each of whom works 7 hours per day. The finishing department has 3 workers, who also work a 7-hour shift. Each pair of J skis require 3.5 labor-hours in the fabricating department and 1 labour-hour in finishing. The D model requires 4 labor-hours in fabricating and 1.5 labour-hours in finishing. The company operates 5 days a week. ABC makes a net profit of $50 on the J model and $65 on the D model. In anticipation of the next ski-sale season, ABC must plan its production of these two models. Because of the popularity of its products and limited production capacity, its products are in high demand, and ABC can sell all it can produce each season. The company anticipates selling at least twice as many D as J models. Answer the following:

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter7: Nonlinear Optimization Models
Section7.7: Portfolio Optimization Models
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(2) ABC is a small manufacturer of two types of popular all-terrain snow skis, the J and the D models. The manufacturing process consists of two principal departments: fabrication and finishing. The fabrication department has 12 skilled workers, each of whom works 7 hours per day. The finishing department has 3 workers, who also work a 7-hour shift. Each pair of J skis require 3.5 labor-hours in the fabricating department and 1 labour-hour in finishing. The D model requires 4 labor-hours in fabricating and 1.5 labour-hours in finishing. The company operates 5 days a week. ABC makes a net profit of $50 on the J model and $65 on the D model. In anticipation of the next ski-sale season, ABC must plan its production of these two models. Because of the popularity of its products and limited production capacity, its products are in high demand, and ABC can sell all it can produce each season. The company anticipates selling at least twice as many D as J models. Answer the following:

a. Define your decision variables and objective function variables.
b. Write your LP model.
c. Determine the feasible region and label the coordinates of the corner
points.
d. Determine how many each model should be produced on a daily basis to
maximize net profit. What is the maximum profit?
e. Based on the optimal solution, how many actual labor-hours are rendered
by the fabrication and finishing departments?
Transcribed Image Text:a. Define your decision variables and objective function variables. b. Write your LP model. c. Determine the feasible region and label the coordinates of the corner points. d. Determine how many each model should be produced on a daily basis to maximize net profit. What is the maximum profit? e. Based on the optimal solution, how many actual labor-hours are rendered by the fabrication and finishing departments?
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