Table 8-3
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 lengths 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.
-Referring to Table 8-3, which of the following constraints would be used?
A) 9T + 12B ≤ 12
B) 1T + 1B ≥ 10
C) 1T + 2B ≤ 12
D) All of the above
E) None of the above

Question

Table 8-3
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 lengths 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. 
-Referring to Table 8-3, which of the following constraints would be used?
A) 9T + 12B ≤ 12 
B) 1T + 1B ≥ 10 
C) 1T + 2B ≤ 12 
D) All of the above 
E) None of the above

Quizplus · Accepted Answer

The constraint equation should limit the amount of varnish and wood available. From the problem statement, we know that one coffee table requires one gallon of varnish and one length of redwood, while one bookcase requires one gallon of varnish and two lengths of redwood. Therefore, the constraint equation for varnish is: Varnish used by coffee tables + varnish used by bookcases ≤ total varnish available. This translates to: T + 2B ≤ 10. Similarly, the constraint equation for redwood is: Redwood used by coffee tables + redwood used by bookcases ≤ total redwood available. This translates to: T + 2B ≤ 12. Thus, the correct constraint equation is 1T + 2B ≤ 12, which is option C.

Table 8-3 Each Coffee Table Produced by Timothy Kent Designers Nets the Nets