The deans' suite hoped to cut costs and decided to perform a total cost analysis on its vodka supplier. Consumption was currently 6,000 bottles per semester and this was predicted to maintain that level for the next few years. Their current source, Byron's, charged $9.25 per bottle and packed 500 bottles in a crate. The cost to ship the crate was $5. Another potential source of vodkas was Pancho's, who charged $9.20 per bottle but could ship only 100 bottles in a crate. Assume that a partial crate may be purchased. At what annual shipping price per crate from Pancho's would the college face equal total costs?

Question

Quizplus · Accepted Answer

To find the annual shipping price per crate from Pancho's that would make the total costs equal, we first calculate the total annual cost from Byron's. Since the consumption is 6,000 bottles per semester, it's 12,000 bottles annually. Byron's charges $9.25 per bottle and ships 500 bottles per crate with a shipping cost of $5 per crate. Therefore, the total cost from Byron's is:$$ \text{Cost of bottles} = 12,000 \times \$9.25 = \$111,000 $$$$ \text{Number of crates} = \frac{12,000}{500} = 24 $$$$ \text{Shipping cost} = 24 \times \$5 = \$120 $$$$ \text{Total cost from Byron's} = \$111,000 + \$120 = \$111,120 $$For Pancho's, the cost of the bottles remains the same except for the price per bottle, which is $9.20. So, the cost of bottles from Pancho's is:$$ \text{Cost of bottles} = 12,000 \times \$9.20 = \$110,400 $$Let $x$ be the shipping price per crate from Pancho's. The number of crates needed for 12,000 bottles, given that each crate holds 100 bottles, is:$$ \text{Number of crates} = \frac{12,000}{100} = 120 $$The total cost from Pancho's, including shipping, would be:$$ \text{Total cost from Pancho's} = \$110,400 + (120 \times x) $$Setting the total costs equal to solve for $x$:$$ \$111,120 = \$110,400 + 120x $$$$ 120x = \$720 $$$$ x = \$6 $$Therefore, at an annual shipping price per crate of $6 from Pancho's, the college would face equal total costs.

The Deans' Suite Hoped to Cut Costs and Decided to Perform