The Lemon Corporation ships frozen orange juice concentrate from processing plants in Eustis and Clermont to distributors in Miami, Orlando, and Tallahassee. Each plant can produce 19 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	$250	$210	$280
Clermont	$220	$230	$300

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.)

MIN:

Subject to:

Eustis

Clermont

Miam

Orlando

Tallahassee

X_ij 0

(b)

Implement the model in a spreadsheet and solve it. What is the optimal solution?

(X₁₁, X₁₂, X₁₃, X₂₁, X₂₂, X₂₃) =

(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.)

(X₁₁, X₁₂, X₁₃, X₂₁, X₂₂, X₂₃) =

(e)

How would the solution change if the plant in Clermont is forced to shut for one day resulting in a loss of two tons of production capacity?

The optimal solution would ________

(f)

What would the optimal objective function value be (in dollars) if the processing capacity in Eustis was reduced by three 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 $