Use the following data for the next three problems

Cost data
Regular time labor cost per hour $10
Overtime time labor cost per hour $15
Subcontracting cost per unit (labor only) $80
Back order cost per unit per period $20
Inventory holding cost per unit per period $10
Hiring cost per employee $500
Firing cost per employee $400

Capacity data
Beginning workforce 40 employees
Beginning inventory 0 units
Beginning back orders (shortages) 0 units
Production standard per unit (hours) 2 hours of labor per unit
Regular time available per period (hours) 160 hours per period per
employee
Overtime time available per period (hours) 30 hours per period per
employee
Number of days per period 20 days
Number of working hours per day 8 hours
Subcontracting No Limit

Demand data
Period 1 3,920 units Period 5 3,800 units
Period 2 2,480 units Period 6 4,340 units
Period 3 2,200 units Period 7 4,820 units
Period 4 3,280 units Period 8 4,600 units

problem #1: Suppose you are designing a level aggregate plan using inventory and back orders (shortages). You are not using any overtime or subcontracting. What will be the production rate per period in the level aggregate production plan?

problem #2: Suppose you are designing a level aggregate plan using inventory and back orders (shortages). You are not using any overtime or subcontracting. How many workers per period (same for every period) are needed for the level aggregate plan?

problem #3: Suppose you are using a chase strategy without inventory and back orders (shortages). In chase strategy you have to meet the demand in every period using regular time production, overtime production and subcontracting. There are 40 workers in each period. When demand is less than the regular time production capacity, you produce only the number of units that are demanded and some of the workers may remain idle. You do not hire and fire workers. How much of the total regular capacity (number of units) remain unused?