The CitruSun Corporation ships frozen orange juice concentrate from processing p
ID: 406862 • Letter: T
Question
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?
Explanation / Answer
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
Objective function: $10 $15 $15 $738,083,564 Decision variables x -138723953 y 71733381.02 Z 69954824.96 Constraints Constraints Three distributors Amount available A 15400 A 260 220 290 15400 B 15600 B 230 240 210 15600 Bounds A 15400 B 15600