Here is a LP problem:
A company produces two kinds of microphones: large and small. The expected demand for the first 3 months of the year is shown below:
The first month : 400 small microphones, 200 large microphones The second month : 500 small microphones, 320 large microphones The third month : 550 small microphones, 400 large microphones
At the regular time of working, 1200 large microphones can be produced in a month and at the overtime, 240 large microphones can be produced.
The production of a large microphone, can be replaced by the production of 2 small microphones. So, if the company produces 199 large micrphones, it should 402 small microphones to meet the demand.
The cost of production of each kind of microphones at the regular time and overtime is shown below:
Small microphone : 60 and 70 units of money (per unit of mic) at the regular time and overtime, respectively.
Large microphone : 80 and 95 units of money (per unit of mic) at the regular time and overtime, respectively.
The cost of inventory is 3 and 5 units of money ( per unit of mic ) for small and large microphones, respectively.
The objective is to meet the demand with the lowest cost.
Provide a Linear-Programming Model for this problem.
Note : My problem is the part that is bolded. I can't find suitable decision variables because I haven't seen any LP problem like that before. ( The replacement of demands is new for me! )
I would appreciate your answers or even hints!