t $1$ Given the following information:

Regular Prod. Capacity $=8,200$ units$/$qtr Regular Prod. Cost $=$ $$18/$unit

Overtime Prod. Capacity $=3,000$ units$/$qtr Overtime Prod. Cost $=$ $$23/$unit

Subcont Prod. Capacity $=5,500$ units$/$qtr Subcont Prod. Cost $=$ $$28/$unit

Inventory Capacity $=7,000$ units$/$qtr Inventory Cost $=$ $$7/$unit$/$qtr

Beginning Inventory $=2,300$ units Backordering Cost $=$ $$19/$unit$/$qtr

$1.$ 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 $=10,500$ units$/$qtr Regular Prod. Cost $=$ $$13/$unit

Beginning work force $=85$ workers Subcont Prod. Cost $=$ $$20/$unit

Production rate$/$worker $=100$ units$/$qtr Inventory Cost $=$ $$9/$unit$/$qtr

Beginning Inventory $=3,000$ units Hiring Cost $=$ $$5,100/$worker

Firing Cost $=$ $$8,400/$worker

$6.$ 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 of $3$ quarters, how many decision

variables would be in the model?

Quarter Demand

$17,500$

$214,300$

$310,800$

Linear programming is to be used to determine a production plan strategy of Level Production,

Overtime, and Subcontracting.

Quarter Demand

$111,200$

$217,800$

$35,900$

Linear programming is to be used to determine a production plan strategy of Level Production,

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