Vollmer Manufacturing makes three materials for sale. The materials are processed by two machines: Machine A and Machine B. The times (in minutes) required by each machine are as follows:

Component	Machine A	Machine B
1	6	4
2	4	5
3	4	2

Machine A is available for 120 hours, and Machine B for 110 hours. Due to partnership agreements and regulations, no more than 200 units of component 3 can be sold, but up to 1,000 units of each of the other components can be sold. Vollmer assumes all material produced will be sold. The company already has an order for 600 units of component 1 that must be satisfied. The profit contributions for components 1, 2, and 3 are $8/lb, $6/lb, and $5/lb, respectively.

1. If time available on Machine A were reduced by 1 minute (all other requirements and limits stay the same as in original model), then what would be the maximum possible profit? (Express answer in $, rounded to 2 decimal places)

2. If time available on Machine A were reduced by 120 minutes (all other requirements and limits stay the same as in original model), then what would be the maximum possible profit? (Express answer in $, rounded to 2 decimal places)

3. If time available on Machine A were reduced by 250 minutes (all other requirements and limits stay the same as in original model), then what would be the maximum possible profit? (Express answer in $, rounded to 2 decimal places)

4. If profit contribution of Material 1 were reduced by $0.15/lb (all other requirements and limits stay the same as in original model), then what would be the optimal production quantity Material 1? (Express answer rounded to 2 decimal places)

5. If profit contribution of Material 1 were reduced by $0.17/lb (all other requirements and limits stay the same as in original model), then what would be the optimal production quantity Material 1? (Express answer rounded to 2 decimal places)

6. What is the minimum increase in the profit contribution of Material 3 (all other requirements and limits stay the same as in original model) that would merit production of any material 3? (Express answer in $/lb, rounded to 2 decimal places)

My Working:

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