DHI recently designed two weight machines for use in commercial gyms. Demonstrations of the machines at a recent trade show resulted in significant dealer interest. As a result, DHI management decided to begin production of the two machines. The two machines, which DHI named the TotalBody1 and the TotlBody2, require different resource inputs.

The TotalBody1 consists of a frame unit with an adjustable seat, a vertical-press station, and a pec-dec station. Each frame produced uses 4 hours of machining and welding time and 2 hours of painting and finishing time. Each vertical-press station requires 2 hours of machining and welding time and 1 hour of painting and finishing time. Each pec-dec station uses 2 hours of machining and welding time and 2 hours of painting and finishing time. In addition, 2 hours are spent assembling, testing, and packaging each TotalBody1 unit. The raw material costs are $450 for each frame, $300 for each vertical-press station, and $250 for each pec-dec station. Packaging costs are estimated to be $50 per unit.

The TotalBody2 consists of a similar frame, vertical-press and pec-dec stations, plus a leg-curl station. Each frame produced uses 5 hours of machining and welding time and 4 hours of painting and finishing time. Each vertical-press station requires 3 hours machining and welding time and 2 hours of painting and finishing time. Each pec-dec station uses 2 hours of machining and welding time and 2 hours of painting and finishing time, and each leg-curl station requires 2 hours of machining and welding time and 2 hours of painting and finishing time. In addition, 2 hours are spent assembling, testing, and packaging each TotalBody2. The raw material costs are $650 for each frame, $400 for each vertical press station, $250 for each pec-dec station, and $200 for each leg-curl station; packaging costs are estimated to be $75 per unit.

For the next production period, management estimates that 3000 hours of machining and welding time, 2250 hours of painting and finishing time, and 700 hours of assembly, testing, and packaging time will be available. Current labor costs are $20 per hour for machining and welding time, $15 per hour for painting and finishing time, and $12 per hour for assembly, testing, and packaging time. The market in which the two machines must compete suggests a retail price of $2400 for the TotalBody1 and $3500 for the TotalBody2, although some flexibility may be available. Authorized DHI dealers can purchase the machines for 70% of the suggested retail price.

DHI's president believes that the unique capabilities of the TotalBody2 can help position DHI as one of the leaders in high-end exercise equipment. Consequently, she has required that the number of units of the TotalBody2 produced must be at least 25% of the total production.

1. Given that DHI can expect revenues of 70% of each machines' retail price, what is the unit profit for each machine?

2. What is the recommended number of TotalBody1 and TotalBody2 machines to produce to maximize profit and meet the resource and managerial constraints?

3. What is the effect on profits of the requirement that the number of units of the TotalBody2 produced must be at least 25% of the total production?

4. Where should efforts be made in order to increase contribution to profits?

5. How like linear programming model and graphical solution would look like ?