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Give and Take Food Services Company delivers fresh sandwiches each morning to vending machines throughout the city. The company makes three kinds of sandwiches ham and cheese, bologna, and chicken salad. A ham and cheese sandwich requires a worker 4.5 hours to assemble, a bologna sandwich requires 4.1 hours, and a chicken salad sandwich requires 5.0 hours to make. The company has 48 available hours each night for sandwich assembly. Vending machine capacity is available for 2,000 sandwiches each day. The profit for a ham and cheese sandwich is GH₵3.5, the profit for a bologna sandwich is GH₵4.2, and the profit for a chicken salad sandwich is GH₵3.7. The company knows from past sales records that its customers buy as many or more of the ham and cheese sandwiches than the other two sandwiches combined, but customers need a variety of sandwiches available, so Metro stocks at most 200 of each.

Question

Give and Take Food Services Company delivers fresh sandwiches each morning to vending machines throughout the city. The company makes three kinds of sandwiches ham and cheese, bologna, and chicken salad. A ham and cheese sandwich requires a worker 4.5 hours to assemble, a bologna sandwich requires 4.1 hours, and a chicken salad sandwich requires 5.0 hours to make. The company has 48 available hours each night for sandwich assembly. Vending machine capacity is available for 2,000 sandwiches each day. The profit for a ham and cheese sandwich is GH₵3.5, the profit for a bologna sandwich is GH₵4.2, and the profit for a chicken salad sandwich is GH₵3.7. The company knows from past sales records that its customers buy as many or more of the ham and cheese sandwiches than the other two sandwiches combined, but customers need a variety of sandwiches available, so Metro stocks at most 200 of each.

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Solution

The company, Give and Take Food Services, delivers fresh sandwiches to vending machines in the city. They offer three types of sandwiches: ham and cheese, bologna, and chicken salad. Each sandwich requires a different amount of time to assemble. A ham and cheese sandwich takes 4.5 hours, a bologna sandwich takes 4.1 hours, and a chicken salad sandwich takes 5.0 hours to make. The company has 48 hours available each night for sandwich assembly.

The vending machines have a capacity of 2,000 sandwiches per day. The profit for a ham and cheese sandwich is GH₵3.5, for a bologna sandwich is GH₵4.2, and for a chicken salad sandwich is GH₵3.7. The company wants to ensure that there is enough variety for customers, so they stock at most 200 of each type of sandwich.

Based on past sales records, the company knows that customers buy as many or more ham and cheese sandwiches compared to the other two types combined.

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