Part $1$ Given the following information:

Regular Prod. Capacity $=8,200$ unit$\frac{s}{q}tr$ Regular Prod. Cost $=$ $$\frac{18}{u}$nit

Overtime Prod. Capacity $=3,000$ unit$\frac{s}{q}tr$ Overtime Prod. Cost $=$ $$\frac{23}{u}$nit

Subcont Prod. Capacity $=5,500$ unit$\frac{s}{q}tr$ Subcont Prod. Cost $=$ $$\frac{28}{u}$nit

Inventory Capacity $=7,000$ unit$\frac{s}{q}tr$ Inventory Cost $=$ $$\frac{7}{u}ni\frac{t}{q}tr$

Beginning Inventory $=2,300$ units Backordering Cost $=$ $$\frac{19}{u}ni\frac{t}{q}tr$

$1.$ Formulate the Objective Function $(note$ that there are $3$ quarters$).$

$2.$ and $3.$ Formulate all Constraints $(standardized).$

$4.$ How many decision variables are $in$ the model?

$5.$ How many constraints are $in$ the model?

Part $2$ Given the following information:

Regular Prod. Capacity $=10,500$ unit$\frac{s}{q}tr$ Regular Prod. Cost $=$ $$\frac{13}{u}$nit

Beginning work force $=85$ workers Subcont Prod. Cost $=$ $$\frac{20}{u}$nit

Production rat$\frac{e}{w}$orker $=100$ unit$\frac{s}{q}tr$ Inventory Cost $=$ $$\frac{9}{u}ni\frac{t}{q}tr$

Beginning Inventory $=3,000$ units Hiring Cost $=$ $$5,\frac{100}{w}$orker

Firing Cost $=$ $$8,\frac{400}{w}$orker

$6.$ Formulate the Objective Function $(note$ which strategies $to$ use$).$

$7.$ and $8.$ Formulate all Constraints $(standardized).$

$9.$ How many constraints are $in$ the model?

$10.If$ there were $6$ months $of$ forecasts, instead $of3$ quarters, how many decision

variables would $bein$ the model?

Quarter Demand

$17,500$

$214,300$

$310,800$

Linear programming $istobe$ used $to$ determine a production plan strategy $of$ Level Production,

Overtime, and Subcontracting.

Quarter Demand

$111,200$

$217,800$

$35,900$

Linear programming $istobe$ used $to$ determine a production plan strategy $of$ Level Production,

Chase Demand, and Subcontracting. Regular Production $is$ the only capacity $limit.$