Please describe the work.
You are a consultant for Woods Restaurants.
At the deli counter, during the busy lunch hour (12-1 pm), the amount of sandwiches (Q) that can be made is determined by the number of workers (L). Suppose each worker makes $6 per hour and sandwiches sell for $4. Further, you have observed the number of workers and quantity of sandwiches over several days and have estimated the following production function:
Q = 4L - 0.25L2
Q1. How many workers should Woods employ during the lunch hour to maximize profits?
(note: consider the value of the marginal product of labor and the marginal revenue product are the same)
Q2. Compute the maximum profit at Woods.
(note: consider that profit involves Total Revenue and Total Costs)
Q3. Compute the marginal revenue product of the sixth worker. Explain why it is or is not profit maximizing to hire a sixth worker.
Q4. Suppose instead that Woods wants to keep the lines as short as possible by maximizing production. How many workers should Woods employ during the lunch hour?
| Control Variable |
Total Benefits |
Total Costs |
Net Benefits |
Marginal Benefit |
Marginal Cost |
Marginal Net Benefit |
| Q |
B(Q) |
C(Q) |
N(Q) |
MB(Q) |
MC(Q) |
MNB(Q) |
| 0.00 |
0.00 |
0.00 |
0.00 |
-- |
-- |
-- |
| 1.00 |
90.00 |
10.00 |
80.00 |
90.00 |
10.00 |
80.00 |
| 2.00 |
170.00 |
30.00 |
140.00 |
80.00 |
20.00 |
60.00 |
| 3.00 |
240.00 |
60.00 |
180.00 |
70.00 |
30.00 |
40.00 |
| 4.00 |
300.00 |
100.00 |
200.00 |
60.00 |
40.00 |
20.00 |
| 5.00 |
350.00 |
150.00 |
200.00 |
50.00 |
50.00 |
0.00 |
| 6.00 |
390.00 |
210.00 |
180.00 |
40.00 |
60.00 |
(20.00) |
| 7.00 |
420.00 |
280.00 |
140.00 |
30.00 |
70.00 |
(40.00) |
| 8.00 |
440.00 |
360.00 |
80.00 |
20.00 |
80.00 |
(60.00) |
| 9.00 |
450.00 |
450.00 |
0.00 |
10.00 |
90.00 |
(80.00) |
| 10.00 |
450.00 |
550.00 |
(100.00) |
0.00 |
100.00 |
(100.00) |