Each coffee table produced by Kevin Watson Designers nets the firm a profit of $8. Each bookcase yields a $6 profit.​ Watson's firm is small and its resources limited. During any given production period ​(of 1 week)​, 9gallons of varnish and 12 lengths of​ high-quality redwood are available. Each coffee table requires approximately 1 gallon of varnish and 1length of redwood. Each bookcase takes 1gallon of varnish and 2 lengths of wood.   The aim of the objective function for Kevin should be to Maximize the objective value.   Part 2 Decision​ variables:      X​ = number of coffee tables produced​ / week      Y​ = number of bookcases produced​ / week   Part 3 Objective​ function:   Z= 8X+6Y       Part 4 Subject​ to:     1X+1Y    ≤ 9    (C1​)       1X+2Y    ≤12   (C2​)       X, Y ≥0       Part 5   On a graph constraints C1 and C2 have been plotted. Using the point drawing tool​, plot all the corner points for the feasible area.   The optimum solution​ is:   X​ =   ​(round your response to two decimal​ places). Y​ =     Optimal solution value Z ​ =

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 17P
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Each coffee table produced by Kevin Watson Designers nets the firm a profit of

$8. Each bookcase yields a $6 profit.​ Watson's firm is small and its resources limited. During any given production period ​(of 1 week)​, 9gallons of varnish and 12 lengths of​ high-quality redwood are available. Each coffee table requires approximately 1 gallon of varnish and 1length of redwood. Each bookcase takes 1gallon of varnish and 2 lengths of wood.

 

The aim of the objective function for Kevin should be to Maximize the objective value.

 

Part 2

Decision​ variables:

     X​ = number of coffee tables produced​ / week

     Y​ = number of bookcases produced​ / week

 

Part 3

Objective​ function:

 

Z=

8X+6Y

   

 

Part 4

Subject​ to:

   

1X+1Y

   ≤ 9

   (C1​)

 

   

1X+2Y

   ≤12

  (C2​)

 

   

X, Y ≥0

   

 

Part 5

 

On a graph constraints C1 and C2 have been plotted. Using the point drawing tool​, plot all the corner points for the feasible area.

 


The optimum solution​ is:

 

X​ =   ​(round your response to two decimal​ places).

Y​ =

 

 

Optimal solution value Z ​ =    (round your response to two decimal​ places).

 

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ISBN:
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Author:
WINSTON, Wayne L.
Publisher:
Cengage,