Question

Champs Sports Bar, State College, PA, has decided to perform a total cost analysis on its vodka supplier in order to cut costs. Consumption is currently 6,000 bottles per year. This demand is predicted to stay at this level for the next few years. The current source, Byron's, charges $9.25 per bottle and can pack 500 bottles in a crate. The cost to ship the crate is $5. Another potential source of vodka is Pancho. Pancho charges $9.20 per bottle and can ship 100 bottles in a crate. Assume that a partial crate may be purchased. Champs Sports Bar will incur equal total costs if Pancho can hold annual shipping price per crate at _____.

Answer 1

Answer:

Champs Sports Bar will incur equal total costs if Pancho can hold annual shipping price per crate at $6

Explanation:

Current consumption = 6000 per year

Byron's Charge

Cost of 1 bottle = $9.25

1 crate contains 500 bottles

6000 bottles would be contained in 12 crates (6000 ÷ 500 = 12)

Cost of 1 crate = $9.25 × 500 = $4625

Shipping price per crate = $5

Cost of 1 crate + shipping price per crate = $4625 + $5 = $4630

Total cost to ship 12 crates (6000 bottles) = 12 × $4630 = $55560

Pancho's charge

Cost of 1 bottle = $9.20

I crate contains 100 bottles

6000 bottles would be contained in 60 crates (6000 ÷ 100 = 60)

Cost of 1 crate = $9.20 × 100 = $920

Let the shipping price per crate be y

Cost of 1 crate + shipping price per crate = ($920 + y)

Total cost to ship 60 crates = 60($920 + y)

To solve for y, equate the two total costs

60($920 + y) = $55560

Divide both sides by 60

$920 + y = $926

y = $926 - $920 = $6

Champs Sports Bar will incur equal total costs if Pancho can hold annual shipping price per crate at $6.