Question

Question:

A TV manufacturer has currently two factories in the US; Iowa and Kansas; and serves to 5 markets: Northeast, Southeast, Midwest, South and West

Iowa has a capacity of 1M, and Kansas has 1.5M.

Each TV sells for $750. It’s expected that the demand will grow within the nextfew years.

Thus, the firm plans to open a new factory in ONE of the two possible locations: Texas OR Indiana, each has a capacity of 1.5M for production

Annual variable cost (i.e. production and shipping) per TV, fixed cost at each location and the demand are given in the Excel provided.

The manufacturer wants to maximize its profit. Which new factory location, Texas OR Indiana, should the firm consider? Explain why?

Input Data						Sale price =>	$750
	Variable Cost (Production and Shipping) ($/unit)					Annual Fixed Cost (million $)	Capacity '000s units
	Northeast	Southeast	Midwest	South	West
Iowa	185	180	175	175	200	150	1000
Kansas	170	190	180	200	220	200	1500
Texas	180	180	185	185	215	200	1500
Indiana	220	220	195	195	175	200	1500
Demand ('000 units)	1050	600	600	450	900
Decision Variables and Constraints
	Quantity Shipped
	Northeast	Southeast	Midwest	South	West	Open/Close (1/0)	Capacity Constraints	Profit
Iowa
Kansas
Texas
Indiana
Demand constraints=>
Answer=>						Objective Function =>

Answer 1

Answer:

The TV manufacturer wants to assess the potential of setting up a new plant either in Iwoa or Kansas. To find a solution, two scenarios have been examined:

• Option 1 (new factory in Texas)
• Option 2 (new factory in Indiana)

Following assumptions have been considered to explore the sales pattern for both options, to minimize the total cost (both fixed and variable). Since fixed cost would same for each production facilities, it is the variable cost which would influence the total cost and deciding factor to assess the profitability.

Constraints:

• Total demand = Total projected sales = 3,600 thousand units
• Total production capacities (considering 2 existing and 1 new plant) = 4,000 thousand units

Thus, total unutilized production capacities = 400 thousand units

Objective Function:

The minimization of the variable (production and shipping) cost

The two scenarios are:

Option 1 (new factory in Texas)

Total Cost of Sales (Fixed +variable)		Units to be sold (optimum projection in '000 units)		Minimum Cost of Sales ('000$)		Profitability Projection (in million)
	Northeast	Southeast	Midwest	South	West	Total Capacity			Northeast	Southeast	Midwest	South	West	Total Capacity			Northeast	Southeast	Midwest	South	West
Iowa	$335	$330	$325	$325	$350	1,000		Iowa	-	-	-	100	900	1,000		Iowa	$0	$0	$0	$32,500	$3,15,000		Total Revenue	$2,700
Kansas	$370	$390	$380	$400	$420	1,500		Kansas	1,050	-	450	-	-	1,500		Kansas	$3,88,500	$0	$1,71,000	$0	$0		Total Cost of Sales	$1,328
Texas	$380	$380	$385	$385	$415	1,500		Texas	-	600	150	350	-	1,100		Texas	$0	$2,28,000	$57,750	$1,34,750	$0		Fixed Cost component for unsold units	80
Total Demand	1050	600	600	450	900			Total	1,050	600	600	450	900	3,600		Total	$1,050	$600	$600	$450	$900		Total Profit	$1,293
																Grand Total	$13,27,500

Option 2 (new factory in Indiana)

Total Cost of Sales (Fixed +variable)		Units to be sold (optimum projection in '000 units)		Minimum Cost of Sales ('000$)		Profitability Projection
	Northeast	Southeast	Midwest	South	West	Total Capacity			Northeast	Southeast	Midwest	South	West	Total Capacity			Northeast	Southeast	Midwest	South	West
Iowa	$335	$330	$325	$325	$350	1,000		Iowa	-	600	51	349	-	1,000		Iowa	$0	$1,98,000	$16,575	$1,13,425	$0		Total Revenue	$2,700
Kansas	$370	$390	$380	$400	$420	1,500		Kansas	1,050	-	450	-	-	1,500		Kansas	$3,88,500	$0	$1,71,000	$0	$0		Total Cost	$1,304
Indiana	$420	$420	$395	$395	$375	1,500		Texas	-	-	99	101	900	1,100		Texas	$0	$0	$39,105	$39,895	$3,37,500		Fixed Cost component for unsold units	80
Total Demand	1050	600	600	450	900			Total	1,050	600	600	450	900	3,600		Total	$3,88,500	$1,98,000	$2,26,680	$1,53,320	$3,37,500		Total Profit	$1,316
																Grand Total	$13,04,000

It is evident, that, considering given assumptions and the constraints, new plant at Indiana would attract less variable cost, thereby less total cost of operation and thereby would ensure maximum profit.