I am writing a linear programming model with two decision variables for the follow scenario but am having trouble structuring it. Here is the set up: A company is going to rent machines that produce widgets and has $\$5000$ to spend. Large machines can produce 200 widgets/month that costs $\$300$ / month. Small machines produce 80 widgets/month and costs $\$1000$ for an initial down payment and $\$100$/month. The company needs to produce 1000 widgets/month. We want to create two linear programs:
- minimize total monthly payments and then
- maximize monthly production capacity
My initial setup is:
$x_1$: Number of large machines
$x_2$: Number of small machines
Minimize monthly payments: $300 x_1 + (100 x_2 + 1000) /x_2$
Constraints:
Cost: $300x_1 + (100x_2 + 1000)/x_2 ≤ 5000$
Widget: $200x_1 + 80x_2 ≥ 1000$
For question 2) Maximize: $200x_1 + 80x_2$ Same constraints.
This should be able to be written as a linear programming problem by the cost constraint is not linear.
What am I missing?