Question

Sycamore Plastics (SP) is a manufacturer of polyethylene plastic pellets used as a raw material by manufacturers of plastic goods around the U.S. SP currently operates four manufacturing centers in Philadelphia, PA; Atlanta, GA; St. Louis, MO; and Salt Lake City, UT. The plants have different capacities and production costs as indicated in the table below.

PLANT	MAXIMUM CAPACITY (× 100,000 LBS.)	PROD. COST (PER 1,000 LBS.)
Philadelphia	7.4	$334.00
Atlanta	9.1	$284.00
St. Louis	12.0	$314.00
Salt Lake City	10.4	$259.00

     SP currently has six contract customers located in New York City; Birmingham, AL; Terre Haute, IN; Dallas, TX; Spokane, WA; and San Diego, CA. Transportation costs between the plants and various customers, as well as contracted demand from each customer, are shown in the table below.

	TRANSPORT COSTS PER 1,000 LBS.
FROM/TO	NYC	BIRMINGHAM	TERRE HAUTE	DALLAS	SPOKANE	SAN DIEGO
Philadelphia	$40	$47	$51	$57	$60	$97
Atlanta	50	37	53	54	62	94
St. Louis	52	55	45	49	47	82
Salt Lake City	67	66	62	52	40	72
Total Demand (× 1,000 lbs.)	538	427	938	602	305	413

a. Create a solver model and find the optimal solution to help SP develop a distribution plan that will minimize costs to supply the customers’ demand. (Enter your answers in terms of cost per 1,000 lbs and shipment quantities per 1,000 lbs. Round your answers to the nearest whole number.)

	CombinedCosts Per 1,000 lbs.
From/To	NYC	Birmingham	Terre Haute	Dallas	Spokane	San Diego
Philadelphia	$	$	$	$	$	$
Atlanta
St. Louis
Salt Lake City

	Solution (× 1,000 lbs.)
From/To	NYC	Birmingham	Terre Haute	Dallas	Spokane	San Diego
Philadelphia
Atlanta
St. Louis
Salt Lake City
Received

	Total Costs
From/To	NYC	Birmingham	Terre Haute	Dallas	Spokane	San Diego
Philadelphia	$	$	$	$	$	$
Atlanta
St. Louis
Salt Lake City
Total cost						$

Answer 1

Spreadsheet model and solution using Solver is as follows:

Combined cost is sum of transport cost and prod. cost

Formulas:

B15 =SUM(B11:B14)   copy to B15:G15

H11 =SUM(B11:G11)   copy to H11:H14

B19 =B3*B11   copy to B19:G22

G23 =SUM(B19:G22)

Total cost = $ 1,085,651