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 21 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. The
company wants to determine the least costly plan for filling their orders for the coming week.
(Suppose the distributors are ok with potentially receiving a surplus of concentrate.) (a)
Formulate an LP model for this problem to minimize cost (in dollars). (Let X ij = tons of
concentrate to ship from plant i to distributor j . Let i = 1 represent Eustis and i = 2 represent
Clermont. Let j = 1 represent Miami, j = 2 represent Orlando, and j = 3 represent Tallahassee.)
(b) Implement the model in a spreadsheet and solve it. What is the optimal solution? ( x 1 1 , x 1
2 , x 1 3 x 2 1 , x 2 2 , x 23 ) = ( (c) Is the optimal solution degenerate? Yes No (d) Is the optimal
solution unique? If not, identify an alternate optimal solution for the problem different from your
answer to part (b). (Enter DNE if the optimal solution from part (b) is the only one.) ( x 1 1 , x 1
2 , x 1 3 x 2 1 , x 2 2 , x 23 ) = ( (e) How would the solution change if the plant in Clermont is
forced to shut for one day resulting in a loss of six tons of production capacity? The optimal cost
for filling the orders would decrease. The optimal cost for filling the orders would increase. The
amount of concentrate being shipped to each distributor from each plant would change, but the
cost for filling the orders would remain the same. The optimal solution would not change at all.
(f) What would the optimal objective function value be (in dollars) if the processing capacity in
Eustis was reduced by seven tons? $ (g) Interpret the reduced cost (in dollars) for shipping from
Eustis to Miami. (Enter your answer as a positive number.) Every additional ton of concentrate
shipped from Eustis to Miami would costs by $.
The City Commission of Nashville has decided to build a botanical gard.pdf
1. The City Commission of Nashville has decided to build a botanical garden and picnic area in the
heart of the city for the recreation of its citizens. The precedence table for all the activities
required to construct this area successfully is as follows: Refer to the legend for the activity that
corresponds to each code. Using the line drawing tool, draw a Gantt chart for activities E through
I of the project.
