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	7.7	$320.00
Atlanta	9.0	$270.00
St. Louis	12.0	$300.00
Salt Lake City	10.3	$245.00

     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	$76	$81
Atlanta	55	42	58	59	78	78
St. Louis	57	60	50	54	63	66
Salt Lake City	72	71	67	57	56	56
Total Demand (× 1,000 lbs.)	521	411	921	596	321	396

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

The Total Expenses made to fulfill all the demand will be our objective cell and as we are required to minimize the expense, we will use the Min target button

The Total components supplied to each cities will be equal to the demand from each cities and this will become our first constraint

The Total components supplied from each plant will be limited by the production capacity and thus should be less than equal to the production capacity. This will become our second constraint.

The solver model is as shown (with formulas in the second screenshot)-

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