# Linear Programming

A manufacturer of excercise equipment will begin production of two types of machines: Body Plus 100 and Body Plus 200.

The Body Plus 100 consists of a frame unit, a press station, and a pec-dec station. each frame produced uses 4 hours of machining and welding time and 2 hours of finishing and painting time. Each press station requires 2 hours of machining and welding time and 1 hour of painting and finishing time, and each pec-dec station requires 2 hours of machining and welding and 2 hours of painting and finishing time. In addition, 2 hours are spent assembling, testing and packaging each body Plus 100. The raw material costs are $450 for each frame, $300 for each press station, and $250 for each pec-dec station. Packaging costs are expected to be $50 per unit.

The Body Plus 200 consists of a frame unit, a press station, a pec-dec station, and a leg-press station. Each frame produced uses 5 hours of machining and welding time and 4 hours of finishing and painting time. Each press station requires 3 hours of machining and welding time and 2 hours of painting and finishing time. Each leg-press station requires 2 hours of machining and welding time and 2 hours of finishing and painting time. In addition, 2 hours are spent assembling, testing and packaging each. The raw materials costs are $650 for each frame, $400 for each press station, $250 for each pec-dec station, and $200 for each leg-press station. Packaging cost is estimated to be $75 per unit.

For the next production period, management estimates that 600 hours of machining and welding time, 450 hours of painting and finishing time, and 140 hours of assembly, testing and packaging time will be available. Current labor costs are $20 per hour for machining and welding, $15 pre finishing and painting time, and $12 for assembly, testing and packaging time.

A retail price of $2400 for each Body Plus 100 and $3500 for each Body Plus 200 are suggested. However, authorized dealers can purchase the machines at 70% of the suggested retail price. Management also believes that the Body Plus 200 can help position the company as one of the leaders in high-end exercise equipment and ordered that the number of Body Plus 200 units produced be at least 25% of the total production.

Question: Make a recommendation to management how many units of each Body Plus 100 and Body Plus 200 to produce. (Use Linear Programming/Optimal Solution to get an answer). Please show all the work as to how you came to the answer. Also please use a table in your work.

Thank You for all of your help.

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#### Solution Summary

A problem is modelled using linear programming and an optimal solution is found. The solution is detailed and well presented.