A firm must plan production levels for the following quarter, determining which products to produce, and how many to produce on each of their 5 available machines.
The quarterly capacities of the machines are 1000, 4000, 6000, 8000, and 10,000. Associated with each product is a fixed marketing cost which must be paid if we produce any of the product. The fixed costs for products 1, 2, 3, 4, and 5 are $585, $605, $635, $815, and $970, respectively. Sales prices for the respective products are $300, $450, $600, $750, and $1000.
Customer demands require production of at least 3000 units of either product 1 or product 3, at least 2000 units of product 2 or product 4, and no more than 5000 units of product 5.
Formulate and solve the firm’s problem.
Please provide calculations and show all work