Calculate the profits gained by increasing labour hour a day

Question

Problems:

Consider the following linear programming problem:  A workshop of Peter's Potters makes vases and pitchers.  Profit on a vase is $3.00;  profit on a pitcher is $4.00.  Each vase requires ½ hour of labor, each pitcher requires 1 hour of labor.  Each item requires 1 unit of time in the kiln.  Labor is limited to 4 hours per day and kiln time is limited to 6 units per day.  Initial and final tableaux are shown in finding the production plan which will maximize profits:  (x = number of vases and y = number of pitchers made per day).

 X    y    u    v    M                                      x    y    u    v    M

½    1    1    0    0   4                               0    1    2    -1   0    2

1     1    0    1    0   6                               1    0   -2    2    0    4                               

-3   -4   0    0    1   0                               0    0    2     2    1    20

(initial)                                                         ( final)

How much surplus labor is there when the optimal plan is in effect?

1. 0 hours
2. 2 hours
3. 4 hours
4. 1 hour
5. None of the above

If labor were increased by one hour a day, profits could be increased to:

1. $24
2. $22
3. $21
4. Not increased
5. None of the above

If labor were increased by one hour a day, the optimal production plan would require how many vases?

1. 2
2. 3
3. 4
4. 1
5. None of the above