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, the solution to the problem is
A) T = 10, B = 0.
B) T = 0, B = 10.
C) T = 0, B = 6.
D) T = 8, B = 2.
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, the solution to the problem is
A) T = 10, B = 0. 
B) T = 0, B = 10. 
C) T = 0, B = 6. 
D) T = 8, B = 2. 
E) None of the above

Quizplus · Accepted Answer

Let T = number of coffee tables produced 
Let B = number of bookcases produced

The constraints are:

1T + 1B ≤ 10 (varnish constraint) 
1T + 2B ≤ 12 (wood constraint)

The objective function is:

9T + 12B (profit)

Using the constraints, we can create a graph:

(0,0) ├───(10,0) 
│              │ 
│              │ 
│              │ 
│              │ 
(8,2)───┴───(0,6)

The vertices are (0,0), (10,0), (0,6), and (8,2). 
Plug in these values to the objective function:

(0,0): 9(0) + 12(0) = 0 
(10,0): 9(10) + 12(0) = 90 
(0,6): 9(0) + 12(6) = 72 
(8,2): 9(8) + 12(2) = 84

The maximum profit is at (8,2), so the solution is T = 8, B = 2.

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