Problem $3($Adapted from Winston, $2004)$: FurnCo produces chairs and tables and must meet the

following demands over the next three months: month $1-15$ chairs, $5$ tables; month $2-20$ chairs, $15$

tables; month $3-10$ chairs, $20$ tables. It requires $2$ labor hours to produce a chair and $5$ labor hours to

produce a table. During each of the next three months, at most $100$ labor hours are available for

production; however up to $50$ additional labor hours can be acquired in each month for a cost of

$$\frac{10}{?}$ hour. The per$-$unit production costs for chairs and tables differ by month and are given in the

following table:

Initially, there is no product in inventory. A holding cost of $$5$ per chair and $$15$ per table is assessed on

product in inventory at the end of months $1$ and $2.$

Part a: Formulate a linear program to meet FurnCo's demand at minimum cost.

Part b: Solve the problem using AMPL$/$CPLEX and report the obtained optimal solution. Attach the text

of your model file and AMPL session.