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

Cosider, a,b,c as this weeks production from Eustis to Miami, Orlando and Tallahassee respectively and, d,e,f as this weeks production from Clermont to Miami, Orlando and Tallahassee respectively.

LPmodel:

a+b+c<=20

d+e+f<=20

a+d=10

b+e=15

c+f=10

a,b,c,d,e,f>=0

Minimize, 260a+220b+290c+230d+240e+310f

b)Optimal Solution as per solver:

c)one constraint will change: i.e d+e+f<=16 (20 tons-4 tons lost)

but the optimal solution as per solver remains the same when solved by solver in excel.

d) if Production at Eustis is reduced by 5 tons then the constraint a+b+c<=20 will change to a+b+c<=15.

then the optimal solution as solved by solver will be: