The Martin-Beck Company operates a plant in St. Louis with an annual capacity of 30,000 units. Product is shipped to regional distribution centers located in Boston, Atlanta, and Houston. Because of an anticipated increase in demand, Martin-Beck plans to increase capacity by constructing a new plant in one or more of the following cities: Detroit, Toledo, Denver, or Kansas City. The estimated annual fixed cost and the annual capacity for the four proposed plants are as follows:

Proposed Plant	Annual Fixed Cost	Annual Capacity
Detroit	$200,000	20,000
Toledo	$280,000	20,000
Denver	$360,000	10,000
Kansas City	$310,000	20,000

The company's long-range planning group developed forecasts of the anticipated annual demand at the distribution centers as follows:

Distribution Center	Annual Demand
Boston	35,000
Atlanta	25,000
Houston	10,000

The shipping cost per unit from each plant to each distribution center is as follows:

	Distribution Centers
Plant Site	Boston		Atlanta		Houston
Detroit	5		2		3
Toledo	4		3		4
Denver	9		7		5
Kansas City	10		4		2
St. Louis	8		4		3

Management wants to run a model that allows for any plant or set of plants to be open so that total cost is minimized. The variable costs for the proposed plant locations are estimated to be the following: Detroit ($4.43), Toledo ($4.32), Denver ($4.64), and Kansas City ($3.88).

We need an estimate of the fixed cost and variable cost at the current St. Louis plant. The file StLouisMB contains 15 observations from previous years that will allow us to estimate these.

Click on the datafile logo to reference the data.

(a)

Use simple linear regression, with total cost as the dependent variable (y) and volume as the independent variable (x). The model y = b₀ + b₁x will give you estimates of b₁ = the per unit variable cost and b₀ = annual fixed cost. Round the fixed cost estimate to the nearest dollar and the variable cost estimate to the nearest cent.

Fixed cost:	$
Variable cost:	$

(b)

Using the data given above for the proposed locations and the fixed and variable costs for St. Louis estimated in part (a), build an optimization model to minimize total cost to meet demand. If the constant is "1", it must be entered in the box.

Let y1	= 1 if a plant is constructed in Detroit; 0 if not
y2	= 1 if a plant is constructed in Toledo; 0 if not
y3	= 1 if a plant is constructed in Denver; 0 if not
y4	= 1 if a plant is constructed in Kansas City; 0 if not
y5	= 1 if a plant is kept in St. Louis; 0 if not
xij	= units shipped from plant i to distribution center j
	where i = 1 (Detroit), 2 (Toledo), 3 (Denver), 4 (Kansas City), 5 (St. Louis) and j = 1 (Boston), 2 (Atlanta), 3 (Houston)

Min	x11	+	x12	+	x13	+	x21	+	x22	+
	x23	+	x31	+	x32	+	x33	+	x41	+
	x42	+	x43	+	x51	+	x52	+	x53	+
	y1	+	y2	+	y3	+	y4	+	y5

s.t.
					x11	+	x12	+	x13	- Select your answer -=Item 26	y1
					x21	+	x22	+	x23	- Select your answer -=Item 31	y2
					x31	+	x32	+	x33	- Select your answer -=Item 36	y3
					x41	+	x42	+	x43	- Select your answer -=Item 41	y4
					x51	+	x52	+	x53	- Select your answer -=Item 46	y5
	x11	+	x21	+	x31	+	x41	+	x51	- Select your answer -><=Item 53
	x12	+	x22	+	x32	+	x42	+	x52	- Select your answer -><=Item 60
	x13	+	x23	+	x33	+	x43	+	x53	- Select your answer -><=Item 67
	xij 0 for all i and j
	y1, y2, y3, y4, y5 {0, 1}

Which plants are open?

- Select your answer -Detroit and DenverDetroit and St. LouisSt. Louis and Kansas CityDetroit, Toledo, and Kansas CityDetroit, Toledo, and St. LouisDetroit, Toledo, and DenverItem 69

What is the total cost to meet demand? Do not round intermediate calculations. If required, round your answer to the nearest dollar.

$