Jeremy Manufacturing Company produces connecting rods for 4- and 6-cylinder automobile engines using the same production line. The cost required to set up the production line to produce the 4-cylinder rods is $1800 and the cost required to set up the production line for the 6-cylinder rods is $3200. Manufacturing costs are $16 for each 4-cylinder connecting rod and $20 for each 6-cylinder connecting rod. The production capacities are 5800 and 7200 for 6 and 4 cylinder rods respectively. The operating budget is $100,000. The selling prices are $55 per 4-cylinder rod and $70 per 6-cylinder rod. What is the optimal number of 4 and 6 cylinder rods that should be produced by the company? Identify the type of integer programming framework (Total Integer, Mixed Integer or Binary) that applies to this problem, develop the appropriate formulation (decision variables, objective function and constraints)
I am having trouble formulating the objective function and constraints. Jeremy Manufacturing Company produces connecting rods for 4- and 6-cylinder automobile engines using the same production line. The cost required to set up the production line to produce the 4-cylinder rods is $1800 and the cost required to set up the production line for the 6-cylinder rods is $3200.
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