Skateboard Supply Chain. Sports of All Sorts produces, distributes, and sells high-quality handcrafted skateboards. Its supply chain consists of three factories that produce the skateboards (located in Detroit, Los Angeles, and Austin). The Detroit and Los Angeles facilities can produce 35,000 skateboards per year, but the Austin plant is larger and can produce up to 70,000 skateboards per year. Skateboards must be shipped from the factories to one of four distribution centers, or DCs, located in Iowa, Maryland, Idaho, and Arkansas. Because of differences in labor rates, the processing and handling charge at each DC is different. These costs per skateboard are $1.34 in Iowa, $1.62 in Maryland, $1.30 in Idaho, and $1.38 in Arkansas. Each distribution center can process (repackage, mark for sale, and ship) at most 50,000 skateboards per year. Skateboards are then shipped from the distribution centers to retailers. Sports of All Sorts supplies three major U.S. retailers: Just Sports, Sports N Stuff, and The Sports Dude. The following tables display the per unit costs for shipping skateboards between the factories and DCs and for shipping between the DCs and the retailers.

Plant	Annual Capacity
Austin	70000
Detroit	35000
Los Angeles	35000

	Shipping Costs ($ per skateboard)
	Iowa	Maryland	Idaho	Arkansas
Detroit	$25.00	$25.00	$35.00	$40.00
Los Angeles	$35.00	$45.00	$35.00	$42.50
Austin	$40.00	$40.00	$42.50	$32.50
	Iowa	Maryland	Idaho	Arkansas
Just Sports	$30.00	$20.00	$35.00	$27.50
Sports'N Stuff	$27.50	$32.50	$40.00	$25.00
The Sports Dude	$30.00	$40.00	$32.50	$42.50

DC	Annual Capacity
Iowa	50000
Maryland	50000
Idaho	50000
Arkansas	50000

DC	Processing Cost ($/skateboard)
Iowa	$1.34
Maryland	$1.62
Idaho	$1.30
Arkansas	$1.38

				Year:
Retailer	1	2	3	4	5	6	7
Just Sports	20300	19100	20000	20400	19800	19500	20500
Sports'N Stuff	49100	49500	50900	49000	50300	49000	49400
The Sports Dude	31600	42000	42500	50400	52400	57900	63400

Sports of All Sorts needs to forecast the demand at each of its four retail locations for next year, and then plan how to produce and distribute its product from the factories through the DCs to the retailers. The file Skateboards contains five tabs: Plant Capacities, Transportation Costs, DC Capacities, DC Processing Costs, and Historical Demand.

Construct a scatter plot for the historical demand for each retailer. Use the historical demand to forecast the future demand for each retailer. For Just Sports and Sports N Stuff, use the average of the historical demands as the forecast for the next year. For The Sports Dude, use simple linear regression to forecast the demand for the next year. Round your forecast to the nearest one thousand units (e.g., if your forecast is 12,303, round to 12,000 for use in part (b).

Construct a linear programming model of the supply chain .

Solve the linear programming model you constructed in part (b). What is the total cost? Which plants are planned to use all of their capacity? Which distribution centers will use all of their capacity?