Production Planning. The management of Hartman Company is trying to determine the amount of each of two products to produce over the coming planning period. The following information concerns labor availability, labor utilization, and product profitability:

Labor$-$Hours Required $($Hours$/$unit$)$

Department

Product $1$

Product $2$

Hours Available

A

$1\mathrm{.}00$

$0\mathrm{.}35$

$100$

B

$0\mathrm{.}30$

$0\mathrm{.}20$

$36$

C

$0\mathrm{.}20$

$0\mathrm{.}50$

$50$

Profit contribution$/$unit

$$30\mathrm{.}00$

$$15\mathrm{.}00$

Develop a linear programming model of the Hartman Company problem. Solve the model to determine the optimal production quantities of products $1$ and $2.$