Table 8-5
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.
T = number of tables produced each week
B = number of bookcases produced each week
-Referring to Table 8-5,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

Quizplus · Accepted Answer

Let's set up the following system of equations based on the given information:
- 1T + 1B ≤ 10 (due to the 10 gallons of varnish available)
- 1T + 2B ≤ 12 (due to the 12 lengths of redwood available)
We also want to maximize the total profit, which is given by: 
- Profit = 9T + 12B 
To solve this problem, we can use graphical analysis or substitution/elimination methods to find the feasible region and the corner points. However, since the answer choices involve integer values, we can simply plug in the values for T and B to see which ones satisfy the system of equations and maximize the profit.

- If T = 10 and B = 0, we have: 
1T + 1B = 10 
1T + 2B = 0 
Profit = 9T + 12B = $90
This point satisfies the first equation, but not the second one.

- If T = 0 and B = 10, we have: 
1T + 1B = 10 
1T + 2B = 20 
Profit = 9T + 12B = $120
This point satisfies the second equation, but not the first one.

- If T = 0 and B = 6, we have: 
1T + 1B = 6 
1T + 2B = 12 
Profit = 9T + 12B = $72
This point satisfies both equations, but we can still do better.

- If T = 8 and B = 2, we have: 
1T + 1B = 9 
1T + 2B = 12 
Profit = 9T + 12B = $108
This point satisfies both equations and gives us the highest profit.

Therefore, the best choice is D, with T = 8 and B = 2.

Table 8-5 Each Coffee Table Produced by Timothy Kent Designers Nets the Nets