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 $1,1,200$ shirts and $1,400$ pairs of pants; month $2,$

$1,300$ shirts and $1,500$ 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 $"0".$

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 decreases $.$