Question

Problem 4: A machine shop purchases electricity at the following rates: First 100 kWh at 13.0 cents per kWh. Next 200 kWh at 11.7 cents per kWh Next 300 kWh at 10.5 cents per kWh. Over 600 kWh at 9.5 cents per kWh. Be accurate to at least two decimal places for all the following problems (a) (3 pts.) The shop uses 392 kWh/month. (a.1) What is the total cost per month (S/month)? (a.2) Average cost (cents/kWh) (a.3) Marginal cost (cents/kWh) (b) (3 pts.) A new machine is installed that will increase total power consumption to 991 kWh/month. (b.I) What is the total cost per month (S/month)? (b.2) Average cost (cents/kWh) (b.3) Marginal cost (cents/kWh)

Answer 1

Problem 4

(a)

Total electricity consumption = 392 kWh/month

Calculate the total cost per month -

Total cost = (100 * $0.13) + (200 * $0.117) + (92 * $0.105)

Total cost = $13 + $23.4 + $9.66

Total cost = $46.06

The total cost per month is $46.06.

Calculate the average cost -

Average cost = Total cost/Total electricity consumed

Average cost = $46.06/392 = $0.1175 or 11.75 cents

So,

The average cost is 11.75 cents/kWh.

Calculate the marginal cost -

Machine shop is consuming a total of 392kWh/month.

The last unit of electricity consumed by the machine shop is coming in the cost bracket which costs 10.5 cents per kWh.

So,

The marginal cost is 10.5 cents/kWh.

(b)

Total electricity consumption = 991 kWh/month

Calculate the total cost per month -

Total cost = (100 * $0.13) + (200 * $0.117) + (300 * $0.105) + (391 * $0.095)

Total cost = $13 + $23.4 + $31.5 + $37.145

Total cost = $105.045

The total cost per month is $105.045.

Calculate the average cost -

Average cost = Total cost/Total electricity consumed

Average cost = $105.045/991 = $0.1059 or 10.59 cents

So,

The average cost is 10.59 cents/kWh.

Calculate the marginal cost -

Machine shop is consuming a total of 991 kWh/month.

The last unit of electricity consumed by the machine shop is coming in the cost bracket which costs 9.5 cents per kWh.

So,

The marginal cost is 9.5 cents/kWh.