The CitruSun Corporation ships frozen orange juice concentrate from processing p
ID: 407007 • 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
A)
So the Linear program objective would be to reduce the Shipping cost from the two production plants to Distribution centers in Miami(M), Orlando(O) and Tallahassee (T)
M = 10, O = 15 , T =10 ........................(a)
and E <=20 and C <=20
Let production in E for Miami be M1 and C as M2 , similarly O1 and O2 and T1 and T2
M1+M2 = M = 10 , O1+O2 = O = 15 AND T1 +T2 = T = 10
and M1 + O1 + T1 <=20 ..............(b)
and M2 + O2 + T2 <= 20 ...............(c)
and Shipping cost equation is = M1*260+M2*230+O1*220+O2*240+T1*290+T2*310 ..................(d)
Equations given in (a),(b),(c),(d)
B)
Using Excel
Using Solver, the oiptimal solution is when
Products for Miami is Produced and shipped from Clermont, M2 = 10
Products for Orlando is Produced and shipped from Eustis , O1 = 15
Products for Tallahassee is Produced and shipped from Eustis, T1 = 5
Products for Tallahassee is Produced and shipped from Clermont, T2 = 5
Which gives minimum shipping cost of = 230*10+ 220*15+ 290*5+310*5 = 8600
C) If the plant at clermont closes down and production falls by 4 tons the solution remains the same as we are only using 15 tons as per the optimal solution agaisnt the capacity of 16 ( 20-4)
Solution remains same
D)
If Eustis is reduced by 5 tons , all the products for tallahassee is sent from Clermont and the LP is as given below
The new shipping cost is 8700 after all the products for tallahassee is sent from Clermont
M O T E 0 15 5 20 20 C 10 0 5 15 20 10 15 10 10 15 10 E 260 220 290 C 230 240 310 Shipping Cost 8600