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Formulating a Linear Programming Equation

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Each coffee table produced by Timothy Kent Designers nets the firm a profit of $9. Each bookcase yields a $12 profit. Kent's firm is small and its resources limited. During any given production period (of 1 week), 10 gallons of varnish and 12 length of high quality redwood are available. Each coffee table requires approximately 1 gallon of varnish and 1 length of redwood. Each bookcase takes 1 gallon of varnish and 2 lengths of wood.

T = number of tables produced each week
B = number of bookcases produced each week

Referring to the above mentioned problem, suppose that this problem requires that you use all the varnish for the week. How would the linear programming representation change?

a. 1B + 1T <= 10 will become 1B + 1T <= 12

b. 1B + 1T <= 10 will be replaced by 1B + 1T >= 10

c. 2B + 1T <= 12 will become 2B + 1T = 12

d. 1B + 1T <= 10 will become 1B + 1T = 10

e. none of the above

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Solution Summary

Each coffee table produced by Timothy Kent Designers nets the firm a profit of $9. Each bookcase yields a $12 profit. Kent's firm is small and its resources limited. During any given production period (of 1 week), 10 gallons of varnish and 12 length of high quality redwood are available. Each coffee table requires approximately 1 gallon of varnish and 1 length of redwood. Each bookcase takes 1 gallon of varnish and 2 lengths of wood.

T = number of tables produced each week
B = number of bookcases produced each week

Referring to the above mentioned problem, suppose that this problem requires that you use all the varnish for the week. How would the linear programming representation change?

a. 1B + 1T <= 10 will become 1B + 1T <= 12

b. 1B + 1T <= 10 will be replaced by 1B + 1T >= 10

c. 2B + 1T <= 12 will become 2B + 1T = 12

d. 1B + 1T <= 10 will become 1B + 1T = 10

e. none of the above

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Because each bookcase (B) uses 1 gallon of varnish (1B) and each table (T) uses 1 gallon of varnish (1T), and there are at most 10 gallons ...

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