A problem that an electricity supply company faces every day is deciding which generators to start up. The company in question has five generators with the characteristics shown in the following table. If a generator produces megawatt-hours (MW-hr), the generator must be started and the fixed start-up cost is incurred. Today at least 7000 MW-hrs must be generated.

	A	B	C	D	mi
Fixed startup cost	$3400	$220	$2750	$1800	$1200
Cost per MW-hr Generated	$6	$5	$7	$7	$8
Maximum Capacity (MW-hr)	2200	1900	2600	1600	3200

Part A: Formulate a binary integer problem that minimizes total cost. Write the complete algebraic form and clearly state the decision variables, objective function, and constraints.

Hint: Some binary variables and large number constraints are needed in this problem.

Decision variables:

A = cost of generator A for fixed start-up cost

B = cost of generator B for fixed start-up cost

C = cost of generator C for fixed startup cost

D = cost of generator D for fixed start-up cost

E = generator cost E for fixed start-up cost

Xa = cost of generator A times Cost per MW-hr Generated

Xb= cost of generator B times Cost per MW-hr Generated

Xc = cost of generator C times cost per MW-hr generated

Xd = cost of generator D times Cost per MW-hr Generated

Xe = generator cost E times Cost per MW-hr Generated

Let ABCDE be binary variables that have a value of 1, if the respective generator is started, otherwise this variable has a value of 0.

Xi be the amount of MW-hr generated by the respective generator

Z mín. = 6Xa + 5Xb+ 7Xc + 7Xd + 8Xe + 3400A + 2200B +27500C + 1800D + 1200E

Subject to:

2200A -Xa ³0

1900B -Xb³ 0

2600C – Xc ³ 0

1600D -Xd³ 0

3200E – Vehicle ³ 0

Xa, Xb, Xc, Xd, Xe ³ 7000

ABCDE = binary

Xa, Xb, Xc, Xd, Xe ³ 0

Part B: Draw your solution graphically.

Make sure my part A is correct and if so, how can I graph that?

Answer rating: 100% (QA)

Solution The formulation of the binary integer problem you provided in Part A seems incorrect Lets correct it and then discuss how to graphically repr... View the full answer