A transportation company is to move goods from three factories to three distribution centers. Information about the move is given below $($see "Supply and Demand" and "Shipping Costs"$).$

Answer the following questions:

a$.$ Draw the network model. $(2$pts$)$

b$.$ What is the Linear Programming Model? $($Be sure to include it in the correct form identifying the objective function and all constraints. $4$pts$)$

c$.$ How many units should be moved from each source to each destination and what is the optimal value of the objective function? Solve using Excel Solver and attach the completed Excel File to receive credit. $(4$pts$)$

Supply and Demand

Source

Supply

Destination

Demand

A

$200$

X

$50$

B

$100$

Y

$150$

C

$150$

Z

$150$

Shipping Costs

$$

Destination

Source

X

Y

Z

A

$3$

$2$

$5$

B

$9$

$10$

$$

C

$5$

$6$

$4$

$$

$($NOTE: Source B cannot ship to destination Z$)$