Continental Motors Scenario

NOTE: This is a challenge problem. It is only worth $10$ points, and you can earn partial credit for progress. This problem will give students who are learning the material very well a chance to demonstrate their skills.

Continental Motors manufactures two different electric motors for sale under contract to a client. Its model GM$3$A is used in the client's food processors and its model GM$3$B is used in the client's blenders. Three times each year the client contracts Continental to place a monthly order for each of the coming four months. Continental has just received the January $-$ April order and must begin its own $4-$month production plan. The number of motors the client ordered is shown in the table below.

Continental must consider several factors:

$-$ They must meet demand for each of the motors in each of the months

$-$ They want to have $450$ units of GM$3$A and $300$ units of GM$3$B in inventory at the end of Aprl, as May demand is expected to be high

$-$ Carrying cost for inventory is $\backslash (\backslash$$ $0\mathrm{.}36\backslash )$ per unit per month for GM$3$A and $\backslash (\backslash$$ $0\mathrm{.}26\backslash )$ per unit per month for GM$3$B$.$ Estimate the monthly inventory as the ending inventory each month

$-$ The company has a no$-$layoff policy, so they want to maintain a production schedule that would require from $2,240$ to $2,560$ hours of labor each month

$-$ The GM$3$A requires $1\mathrm{.}3$ hours of labor per unit and the GM$3$B requires $0\mathrm{.}9$ labor hours per unit

$-$ The warehouse is limited to an inventory of $3,300$ units $($of GM$3$A and GM$3$B combined$)$ at the end of each month

$-$ Production costs are $\backslash (\backslash$$ $20\backslash )$ per unit for GM$3$A and $\backslash (\backslash$$ $15\backslash )$ per unit for GM$3$B$,$ however each of these costs will increase by $\backslash (10\backslash \%\backslash )$ on March $1$ due to a new labor agreement

Determine how many units of each product Continental should produce each month in order to