The Sentry Lock Corporation manufactures a popular commercial security lock at plants in Macon, Louisville, Detroit, and Phoenix. The per unit cost of production at each plant is $35.50, $37.50, $39.00, and $36.25, respectively, while the annual production capacity at each plant is 18,000, 15,000, 25,000, and 20,000, respectively. Sentrys locks are sold to retailers through wholesale distributors in seven cities across the United States. The unit cost of shipping from each plant to each distributor is summarized in the following table along with the forecasted demand from each distributor for the coming year.

	Unit Shipping Cost to Distributor in
Plants	Tacoma	San Diego	Dallas	Denver	St. Louis	Tampa	Baltimore
Macon	$2.50	$2.75	$1.75	$2.00	$2.10	$1.80	$1.65
Louisville	$1.85	$1.90	$1.50	$1.60	$1.00	$1.90	$1.85
Detroit	$2.30	$2.25	$1.85	$1.25	$1.50	$2.25	$2.00
Phoenix	$1.90	$0.90	$1.60	$1.75	$2.00	$2.50	$2.65
Demand	8,500	14,500	13,500	12,600	18,000	15,000	9,000

Sentry wants to determine the least expensive way of manufacturing and shipping locks from its plants to the distributors. Because the total demand from distributors exceeds the total production capacity for all the plants, Sentry realizes it will not be able to satisfy all the demand for its product but wants to make sure each distributor will have the opportunity to fill at least 80% of the orders received.

a) Identify and list the decision variables

b) Identify and list the objective function

c) Identify and list the constraints