Question

José Martinez of El Paso has developed a polished stainless-steel tortilla machine that makes it a “showpiece” for display in Mexican restaurants. He needs to develop a 5-month aggregate plan. His forecast of capacity and demand follows:

	Month 1	Month 1	Month 1	Month 1	Month 1
Demand	150	160	130	200	210
Capacity
Regular	150	150	150	150	150
Overtime	20	20	10	10	10

Additional information: Subcontracting: 100 units available over the 5-month period, Beginning inventory: 0 units

Costs:

Regular time cost per unit = $100

Overtime cost per unit = $125

Subcontract cost per unit = $135

Inventory holding cost per unit = $3

Assume that back-orders are not permitted.

a. Using the transportation method, what is the total cost of the optimal plan?                            [ Select ]                       ["$90,140", "$86,100", "$88,150", "$85,500"]      

b. Does any regular time production go unused?                            [ Select ]                       ["cannot determine", "no", "yes"]         If so/not, how much is used or not used? 50 units

c. What is the total cost of the plan if ending inventory required for the next planning period is: 20 units (include holding costs in the overall calculation)?           [ Select ]                       ["$88,150", "$90,850", "$90,910", "$91,900"]      

please answer all the questions with the right answer thanks

Answer 1

Already Solved:

Produce in \ Used in	M1	M2	M3	M4	M5	Total	Capacity
Beginning inventory	0	0	0	0	0	0	0
M1 reg time	150	0	0	0	0	150	150
M1 overtime	0	0	0	0	0	0	20
M1 subcontract	0	0	0	0	0	0	999
M2 reg time	0	150	0	0	0	150	150
M2 overtime	0	10	10	0	0	20	20
M2 subcontract	0	0	0	0	0	0	999
M3 reg time	0	0	110	40	0	150	150
M3 overtime	0	0	10	0	0	10	10
M3 subcontract	0	0	0	0	0	0	999
M4 reg time	0	0	0	150	0	150	150
M4 overtime	0	0	0	10	0	10	10
M4 subcontract	0	0	0	0	0	0	999
M5 reg time	0	0	0	0	150	150	150
M5 overtime	0	0	0	0	10	10	10
M5 subcontract	0	0	0	0	50	50	999
Total	150	160	130	200	210
Demand	150	160	130	200	210
Total Cost	$88,150

(a)

Total cost = $88,150

(b)

As we can see in the 'Total' column, all of the regular time capacity is utilized

(c)

Slightly change the formulation and keep the same solver input:

Solution:

Produce in \ Used in	M1	M2	M3	M4	M5	Total	Capacity
Beginning inventory	0	0	0	0	0	0	0
M1 reg time	150	0	0	0	0	150	150
M1 overtime	0	0	0	0	0	0	20
M1 subcontract	0	0	0	0	0	0	999
M2 reg time	0	150	0	0	0	150	150
M2 overtime	0	10	0	10	0	20	20
M2 subcontract	0	0	0	0	0	0	999
M3 reg time	0	0	120	30	0	150	150
M3 overtime	0	0	10	0	0	10	10
M3 subcontract	0	0	0	0	0	0	999
M4 reg time	0	0	0	150	0	150	150
M4 overtime	0	0	0	10	0	10	10
M4 subcontract	0	0	0	0	0	0	999
M5 reg time	0	0	0	0	150	150	150
M5 overtime	0	0	0	0	10	10	10
M5 subcontract	0	0	0	0	70	70	999
Total	150	160	130	200	230
Demand	150	160	130	200	230
Total Cost	$90,910

Total cost = $90,910