# 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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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 ...

#### Solution Summary

Linear programming and the simplex methods for analyzed. The surpluses of pitchers are computed.