Develop a linear program to find an optimal plan. We define the following variables: I_i: inventory at the end of period i. O_i: number of units produced by overtime production in period i. R_i: number of units produced by regular production in period i. A correct linear programming formulation is:

	a.	Minimize Cost = 3I1 +3I2 +3I3 + 3I4 Subject to I0 +O1 +R1 d1 =I1 I1 +O2 +R2 d2 =I2 I2 +O3 +R3 d3 =I3 I3 +O4 +R4 d4 =I4 Ri 3000, i = 1,2,3,4 Ri, Oi, Ii 0, i = 1,2,3,4
	b.	Minimize Cost = 3I1 +3I2 +3I3 +3I4 +10O1 +10O2 +10O3 +10O4 Subject to I0 +O1 +R1 d1 =I1 I1 +O2 +R2 d2 =I2 I2 +O3 +R3 d3 =I3 I3 +O4 +R4 d4 =I4 Ri 3000, i = 1,2,3,4
	c.	Minimize Cost = 3I1 +3I2 +3I3 +3I4 +10O1 +10O2 +10O3 +10O4 Subject to I0 +O1 +R1 d1 =I1 I1 +O2 +R2 d2 =I2 I2 +O3 +R3 d3 =I3 I3 +O4 +R4 d4 =I4 Ri, Oi, Ii 0, i = 1,2,3,4
	d.	Minimize Cost = 3I1 +3I2 +3I3 +3I4 +10O1 +10O2 +10O3 +10O4 Subject to I0 +O1 +R1 d1 =I1 I1 +O2 +R2 d2 =I2 I2 +O3 +R3 d3 =I3 I3 +O4 +R4 d4 =I4 Ri 3000, i = 1,2,3,4 Ri,Oi,Ii 0, i = 1,2,3,4
	e.	Minimize Cost = 10O1 + 10O2 + 10O3 + 10O4 Subject to I0 + O1 + R1 d1 = I1 I1 +O2 +R2 d2 =I2 I2 +O3 +R3 d3 =I3 I3 +O4 +R4 d4 =I4 Ri 3000, i = 1,2,3,4 Ri, Oi, Ii 0, i = 1,2,3,4

Questions 22-24 refer to the following problem: A manufacturer has the following information on its major product group: Regular-time production capacity = 3,000 units/period Overtime production cost = $10/unit Inventory costs = $3/unit/period (based on the ending inventory) Beginning inventory, lo = 0 units Backlogs are not allowed. There are no layoffs or hirings, since the manufacturer wants to maintain a stable work force. Period Demand(units) 1 d 1 = 1,500 2 d 2 = 2,1 00 3 d 3 = 3,600 4 d 4 = 5,2 00 Develop a level production plan that yields zero inventory at the end of period 4. In doing your calculations, you could use a table like the one shown below. Season Demand Production Ending Rate inventory Regular production Units done by rate overtime 0 1 2 14 What is the total cost resulting from this plan? a. $28,000 b. $20,300 c. $22,900 d. $30,000 O e. $35,100 QUESTION 23 Develop a chase production plan that yields zero inventory at the end of each period. In doing your calculations, you could use a table like the one shown below. Season Demand Production Ending Rate inventory Regular production Units done by rate overtime o 2 What is the total cost resulting from this plan? O a. $28,000 b. $20,300 OC. $22,900 d. $30,000 O e. $35,100