$(3)$ An aggregate plan for four upcoming quarters cases of a fruit drink is to be developed. Demand for

each quarter, production quantity and ending inventory for the previous quarter, Quarter $0,$ are

provided. The relevant costs are:

Beginning inventory is $100$ cases. Inventory cost$/$case$/$quarter is $$5.$

Regular time production capacity is $1800$ cases and overtime production is limited to $300$

cases.

Regular time production cost is $$\frac{30}{?}$ case. Overtime production cost is $$\frac{45}{?}$ case.

An unlimited number of cases can be subcontracted at a cost of $$\frac{50}{?}$ case.

Cost of labor fluctuation due to changes in production level from quarter to quarter are

accounted for as: $$4$ per unit of increase in production level and $$8$ per unit of decrease in

production level.

$($a$)$ Develop an aggregate plan using a 'produce to demand' strategy. Provide answers to the

questions that follow after completing the aggregate plan in the table below.

i$.[5$ points$]$ What is the total of production level increases? $,{900}_{?}$

ii$.[5$ points$]$ What is the total of production level decreases? $,1300$

iii. points