Vela is building electric cars in their plant Edmonton. Edmonton has a monthly production of $400$ cars. The newly built electric cars are then transported to the dealerships in Calgary, Canmore, and Lethbridge. Electric cars are becoming popular, and the provincial government of Alberta is offering generous rebates to encourage their adoption. Because of the rebate option, the demand for electric cars has increased. The company plans to expand its capacity by constructing new plants in one or more of the following cities: Banff, Edson, Hinton, or Red Deer. Banff's estimated annual fixed cost is $$30$ million, with a monthly capacity of $240$ cars. Edson's is $$60$ million, with a monthly capacity of $300$ cars. Hinton's is $$80$ million, with a monthly capacity of $350$ cars. Red Deer's is $$70$ million, with a monthly capacity of $250$ cars. The company consultants predict that the estimated monthly demand for the cars at the dealership has increased. Calgary needs $290$ cars, $250$ cars for Canmore, and $500$ cars for Lethbridge.

The transportation charges $($in dollars$)$ per car from each plant to each dealership are shown below.

Plants

Banff

Edson

Hinton

Calgary

$500$

$400$

$200$

Canmore

$800$

$1100$

$500$

Lethbridge

$1300$

$600$

$900$

Red Deer

Edmonton

$200$

$300$

$1000$

$700$

$1200$

$500$

a$)$ Draw a network representation of this problem.

b$)$ Define all of the decision variables clearly.

c$)$ Formulate the objective function clearly.

d$)$ Clearly specify all the constraints such that only constants appear on the right$-$hand sides of

constraints.

e$)$ Write a single constraint showing that if Vesla is constructing in Edson, then Vela must also

construct in Hinton or Red Deer or both.

f$)$ Write a single constraint that if Vela can construct in Banff, then Vesla must also construct in

Hinton.

g$)$ Write a single constraint: if Vesla can construct in Banff, then Vesla cannot construct in Red

Deer.