# Linear Programming and the Simplex methods : Surpluses

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?

a. 0 hours
b. 2 hours
c. 4 hours
d. 1 hour
e. None of the above

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

a. \$24
b. \$22
c. \$21
d. Not increased
e. None of the above

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

a. 2
b. 3
c. 4
d. 1
e. None of the above

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