# You buy 3,000 pairs of sunglasses at the beginning of the summer. You estimate that 20 percent of them will have to be put on your "bargain table" at the end of the season on which everything is...

You buy 3,000 pairs of sunglasses at the beginning of the summer. You estimate that 20 percent of them will have to be put on your "bargain table" at the end of the season on which everything is priced at $1.00.

Generally, about thirty percent of the "bargain table" items will be damaged or broken and will have to be thrown away. The glasses cost you $1.25 per pair and you want an average markup of 36% based on selling price.

Round your final answer properly to two decimal places.

a) What is the total cost (TC)?

$ the right answer is 3750.00

b) What is the total sales (TS) given the total cost (TC) and the average mark up (TM)?

$ the wrong answer i got is 5100.00

c) At what price must they start selling the sunglasses?

$ the wrong answer i got is 1.95

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### 1 Answer

You buy 3000 sunglasses at a cost of $1.25 each. You know that 20% of the sunglasses will end up on your "bargain table" priced at $1. Additionally, you know that 30% of items on the "bargain table" are defective and must be destroyed. You would like to set your selling price to achieve an average markup of 36% (based on the sale price.)

(a) The total cost for the sunglasses is 3000($1.25)=$3750

(b) There will be 600 (3000 times 20%) sunglasses on the bargain table. Of those 600, 180 will be destroyed. So you will sell 2400 sunglasses at full price and 420 sunglasses at $1.

Markup can be calculated by `"Markup"=("sales"-"cost")/"cost"` ; `("sales"-3750)/3750=.36`

This is implies that the total sales should be $5100.

However the tagline indicates that we are looking for effective markup -- depending on the usage this is probably the profit margin (as opposed to the profit percentage.) To calculate the profit margin we have `"ProfitMargin"=("Totalsales"-"cost")/("Totalsales")`

`"PM"=("sales"-3750)/("sales")`

`.36=("sales"-3750)/"sales"`

`3750=.64"sales"`

`"sales"=5859.38`

Assuming that the question is asking for profit margin (also called the markon percent) then we need total sales of $5859.38

(c) To determine the retail sales price: the total sales should be 5859.38, there are 2400 sold at full price and an additional 420 sold for $1.

2400x+420=5859.39 ==> the retail sales price should be $2.27

(Using the $5100 from above gives a retail price of $1.95).

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