A customer at a 7-11 store selected four items to buy, and was told
that the cost was $7.11. He was curious that the cost was the same
as the store name, so he inquired as to how the figure was derived.
The clerk said that he had simply multiplied the prices of the four
individual items. The customer protested that the four prices
should have been ADDED, not MULTIPLIED. The clerk said that that
was OK with him, but, the result was still the same: exactly $7.11.

Too late, I have an answer, I'm just working on writing out the explanation 

Explanation pending, it's $1.20, $1.25, $1.50, $3.16

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Explanation:

(Prime) Factors of 711 are 3, 3 and 79, so in cents, 3 * 3 * 79 would be 711. We are however working in dollars to avoid fscking up the decimals, so $3 * $3 * $79 is 100 times too much, but $3 * $3 * $0.79 = $7.11

We need 4 items, so throw in a $1 -- $1 * $3 * $3 * $0.79
$1 + $3 + $3 + $0.79 = $7.79, so we need to reduce the sum while maintaining the product. To do this, we can divide/multiple two of the values by the same thing. This will add to the total more than it takes away, or vice versa

So, multiply $0.79 by 2, and dividing $3 by 2, we get $1, $1.50, $3, $1.58, product = $7.11, sum = $7.08

Which is pretty goddamn close, so I used my magic spreadsheet powers to expound out my options for multiplying/dividing things by various numbers, and how much effect that would have on the sum and looked for small-ish changes. Halving the other $3, and doubling the $1.58 increases the total by 8 cents, bringing us to $1, $1.50, $1.50, $3.16, sum = $7.16

At this point I realised that having my options for numbers to multiply/divide by go up to 15 was probably redundant (sledgehammer to a nut style) and changed it to look at multiplying/dividing by numbers in steps of 0.25, looking for one that would effect a change of 5 cents.

Low and behold, multiplying $1 by 1.2 and dividing $1.50 by the same gives us the desired result. Actually so does multiplying $1 by 1.25, and dividing $1.50 by the same, you get the same 2 values either way.

+1 Super-King ...does not matter how you got this answer but is correct

Gee, such an awesome explanation and FLG just discards it....I applaud your deductive reasoning SK!