True Shaft manufactures a variety of golf products, including shafts for golf clubs. They currently have five different types of shaft in their product line. The production manager, J.P. Weaver, has to determine how many of each type to produce during the next production period. The shafts will require casting, tooling, and finishing in each of three production facilities. the time required for each shaft type, and the total hours available, are listed in hte following table:
P1000 Q45 R380 S4.2 T11 Hours Avail.
Casting .4 .6 .1 .3 1.0 1200
Tooling .15 .20 .07 .12 .25 800
Finishing .06 .03 .08 .05 .11 600
For each shaft type, Weaver has determined the maximum that True shaft would be likely to sell, the profit per unit, and the minimum allowable production lot, should any of a particular shaft type be produced at all. (There is the option of not producing one or more of the shaft types during the upcoming production run.) These values can be found below
Shaft Type Maximum Production Profit $/Unit Minimum Batch Size
P1000 600 7.00 100*
Q45 450 8.25 100
R380 1200 5.40 300
S 4.2 900 6.70 250
T 11 250 12.20 50
*This means that for all shaft types, they may produce none at all, but if they produce, they must produce between 100 and 600 of these shafts.
Mr. Weaver would like to maximize profit, given the resources available. Must produce a linear program with following components: variable definitions, objective function and constraints.