Question

Robert is looking to buy a deep fryer. He has narrowed his search down to two models. The following table gives the details of the prices, cost per use in electricity and oil, and lifespan of the two models Robert is considering to purchase.

Brand
Brand P
Brand Q
Price
$144.00
$37.50
Avg. Cost/Use
$0.49
$0.75
Lifespan
6 years
2 years

Robert plans on using his deep fryer about eight times per month. After six years, which brand will have the lower lifetime cost, and by how much?

Hint: Assume that either deep fryer can be repurchased at the same price, if needed to provide the desired length of service.

a.
Brand P will be $118.26 cheaper than Brand Q.
b.
Brand P will be $149.76 cheaper than Brand Q.
c.
Brand Q will be $184.50 cheaper than Brand P.
d.
Brand Q will be $31.50 cheaper than Brand P.

Answer 1

Compute total uses: 6 years × 12 months/year × 8 uses/month = 576 uses.

Brand P:
- Purchase once: $144.00
- Usage cost: 576 × $0.49 = $282.24
- Total = $144.00 + $282.24 = $426.24

Brand Q:
- Needs replacement every 2 years → 3 purchases: 3 × $37.50 = $112.50
- Usage cost: 576 × $0.75 = $432.00
- Total = $112.50 + $432.00 = $544.50

Difference: $544.50 − $426.24 = $118.26

So Brand P will be $118.26 cheaper than Brand Q. (Answer: a)