A textile company produces shirts and pants. Each shirt requires two square yards of cloth, and each pair of pants requires three square yards of cloth. During the next two months the following demands for shirts and pants must be met $($on time$)$: month $1,1,000$ shirts and $1,500$ pairs of pants; month $2,1,200$ shirts and $1,400$ pairs of pants. During each month the following resources are available: month $1,9,000$ square yards of cloth; month $2,6,000$ square yards of cloth. In addition, cloth that is available during month $1$ and is not used can be used during month $2.$ During each month it costs $$8$ to produce an article of clothing with regular$-$time labor and $$16$ with overtime labor. During each month a total of at most $2,500$ articles of clothing can be produced with regular$-$time labor, and an unlimited number of articles of clothing can be produced with overtime labor. At the end of each month, a holding cost of $$3$ per article of clothing is incurred.

a$.$ Determine how to meet demands for the next two months $($on time$)$ at minimum cost. Assume that $100$ shirts and $200$ pairs of pants are already in inventory at the beginning of month $1.$ If your answer is zero, enter $"0".$

$\backslash$table$[[,$Regular time production,Overtime production$],[,$Month $1,$Month $2,$Month $1,$Month $2],[$Shirts produced$],[$Pants produced,,,,$],[$Total cost:$,$$$,,,]]$

b$.$ Use a two$-$way SolverTable to investigate the effect on total cost of two simultaneous changes. The first change is to allow the ratio of overtime to regular$-$time production cost $($currently $$\frac{16}{\text{\$}}8=2)$ to decrease from $20\%$ to $80\%$ in increments of $20\%,$ while keeping the regular time cost at $$8.$ The second change is to allow the production capacity each month $($currently $2,500)$ to decrease by $10\%$ to $50\%$ in increments of $10\%.$ The idea here is that less regular$-$time capacity is available, but overtime becomes relatively cheaper. Is the net effect on total cost positive or negative?

For low ratios of overtime to regular time production cost, as production capacity decreases, cost $($

For high ratios of overtime to regular time production cost, as production capacity decreases, cost

As the ratio of overtime to regular time production cost increases, cost $$