The CitruSun Corporation ships frozen orange juice concentra

The CitruSun Corporation ships frozen orange juice concentrate from processing plants

in Eustis and Clermont to distributors in Miami, Orlando, and Tallahassee. Each plant

can produce 20 tons of concentrate each week. The company has just received orders

of 10 tons from Miami for the coming week, 15 tons for Orlando, and 10 tons for

Tallahassee. The cost per ton for supplying each of the distributors from each of the

processing plants is shown in the following table.

Miami Orlando Tallahassee

Eustis $260 $220 $290

Clermont $230 $240 $310

The company wants to determine the least costly plan for filling their orders for the

coming week.

a) Formulate an LP model for this problem.

b)Implement the model in an Excel spreadsheet and solve it. What is the optimal

solution?

c) How would the solution change if the plant in Clermont is forced to shut for one

day resulting in a loss of four tons of production capacity?

d) What would the optimal objective function value be if the processing capacity in

Eustis were reduced by five tons?

Solution

Answer:

Let us suppose the the cost per unit to make the least costly product be:

x for miami

y for orlando

z for Tallahassee

Therefore the objective function will be:

10x + 15y + 15z = C (Minimize)

subject to constraints:

260x + 220y + 290z <= 15,400

230x + 240y + 310z <= 15,600