A company manufactures three different types of pipe fitting: tees, elbows, and splicers. Daily production of these parts are limited by the availability of lathe time, grinder time, and labor availability as indicated in the table below:
Products | Availability of Resource | |||
Resources | 100 Tees | 100 Elbows | 100 Splicers | |
Person hours | 6 | 4 | 5 | 24 |
Lathe hours | 1 | 2 | 1 | 8 |
Grinder hours | 2 | 1 | 0 | 12 |
Profit per 100 units | $700 | $550 | $480 |
|
For example, each 100 units of tees requires 6 person hours to produce, include 1 hour of lathe time and 2 hours of grinder time. All the tees that are made can be sold for $700 per 100 units. A total of 24 person hours, 8 lathe hours, and 12 grinder hours are available on a given day.
(a) Formulate a linear program that will suggest a production policy for maximizing daily profit.
(b) Augment your constraint set by adding the appropriate slack and surplus variables. List, in tabular form, all extreme point solutions of the solution space for this problem.
(c) Graph the feasible region in decision space for this problem and label the feasible extreme points to correspond to those presented in part (b).
(d) Solve this linear program using the simplex algorithm summarizing the results of each simplex pivot as a basis representation or simplex tableau. Explain fully your justification for selecting variables to enter and leave the basis for each iteration.
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