For the following integer programming problem, state clear decision variable def

Question

For the following integer programming problem, state clear decision variable definitions and the objective function and constraints:

Bus Works Inc. produces three types of specialty busses with realtively low demands and high profit margins (Metro, Rural and LiftAssist). Data for each of the busses is given in the table below. The resources available over the next year are as follows: 15,000 tons of steel; and 105,000 hours of labor. For production of the Metro to be economically feasible, at least 450 busses would need to be made. Similarly, minimum production quantities for the Rural and LiftAssist are 400 adn 250, respectively. Formulate an Integer Programming to find the product mix that will maximize the contribution to profit.

Metro Rural LiftAssist Steel Required (tons) 8 4 5 Labor Required (hours 110 60 90 Contribution to profit ($/unit) $25,000 $17,000 $20,000

Explanation / Answer

Decision Variables:

x --> Number of Metro Busses

y --> Number of Rural Busses

z --> Number of LiftAssist Busses

Objective function:

Maximize z = 25000x + 17000y + 20000z

Constraints:

8x + 4y + 5z < 15000

1110x + 60y + 90z < 105000

x > 450

y > 400

z > 250

x, y, z > 0

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