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	7.5	$326.00
Atlanta	9.5	$278.00
St. Louis	12.5	$306.00
Salt Lake City	10.3	$251.00

     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	$45	$52	$56	$62	$77	$80
Atlanta	55	42	58	59	79	77
St. Louis	57	60	50	54	64	65
Salt Lake City	72	71	67	57	57	55
Total Demand (× 1,000 lbs.)	524	420	932	595	350	450

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

(a) Calculate combined costs by adding the production cost for each plant and transport cost from each plant to customers.

	Combined Costs Per 1000 lbs.
FROM/TO	NYC	BIRMINGHAM	TERRE HAUTE	DALLAS	SPOKANE	SAN DIEGO
Philadelphia	371	378	382	388	403	406
Atlanta	333	320	336	337	357	355
St. Louis	363	366	356	360	370	371
Salt Lake City	323	322	318	308	308	306

Formulas:

B15 =SUM(B11:B14)   copy to B15:G15

H11 =SUM(B11:G11)   copy to H11:H15

B17 =SUMPRODUCT(B11:G14,B3:G6)

	Total costs
FROM/TO	NYC	BIRMINGHAM	TERRE HAUTE	DALLAS	SPOKANE	SAN DIEGO
Philadelphia	15,211	0	0	0	0	0
Atlanta	160,839	134,400	0	15,839	0	0
St. Louis	0	0	331,792	114,480	0	0
Salt Lake City	0	0	0	70,840	107,800	137,700
Total Costs						1,088,901