The Williams Calculator Company manufactures two kinds of calculators: the TW 100 and TW 200. The assembly process requires three workers. The assembly times are as follows:

- TW 100: X minutes per unit
- TW 200: Y minutes per unit

The company policy is to balance workloads on all assembly jobs. Management wants to schedule work so that no assembler will have more than 30 minutes more work per day than other assemblers. This means that in a regular 8-hour shift, all assemblers will be assigned at least 7.5 hours of work.

Additionally, the company must produce more TW 100 calculators than twice the amount of TW 200 calculators since the demand for TW 100 is usually more than two times the demand for TW 200 in the market.

If the firm makes a $50.00 profit for each TW 100 and a $70.00 profit for each TW 200, how many units of each type of calculator should be produced per day?

The problem is about optimising the production of two types of calculators at the Williams Calculator Company, considering constraints on assembly times and product demand. The solution involves the usage of linear programming, but specific numerical values cannot be provided without the provided assembly times.

Explanation:

This question is about linear programming, a field in Math where we try to optimise a certain outcome (in this case profits) given certain constraints (workload balance, demand ratio etc). Three variables can be identified: the number of TW 100 calculators produced (let's call it 'x'), the number of TW 200 calculators produced ('y'), and the total profit ('P'). Since it's given that TW 100 needs to be produced twice as much as TW 200, we can express it as x = 2y.

The total profit can be calculated as P = 50x + 70y. We also know each worker must work for at least 7.5 hours but no more than 8.5 hours i.e., the combined assembly times for TW 100 and TW 200 must fall within this limit for each worker. The exact values for the assembly times are missing in the problem hence the specific numerical solution is not possible but theoretically, we would substitute the values and solve for x and y.

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