A customer at a 7-11 store selected four items to buy, and was told that the cos
ID: 3147271 • Letter: A
Question
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.
What were the prices of the four items? You MUST create a Solver model to answer this question. There are NO FRACTIONAL pennies allowed for the prices. Remember, cell formatting has NOTHING to do with the actual value contained in a cell. Submit your Excel file which includes your Solver model and an explanation regarding how you solved the problem.
Warning: While it's not terribly difficult to come up with A model, it can be very difficult to come up with a formulation and set of Solver options that actually lead to the correct answer. There is only one correct set of four prices. Again, a price of 2.34576 is NOT valid as it can only contain pennies, NOT fractional pennies. Simply rounding the four prices is not the answer either. If you do that, sum up the four rounded prices and take the product of the four rounded prices and, unless you got lucky and found the one solution, the sum and/or product will NOT equal 7.11 EXACTLY.
Explanation / Answer
The prices are: $1.20, $1.25, $1.50, and $3.16 $7.11 is not the only number which works. Here are the first 160 such numbers, preceded by a count of distinct solutions for that price. Note that $7.11 has a single, unique solution. 1 - $6.44 1 - $7.83 2 - $9.20 3 - $10.89 1 - $6.51 1 - $7.86 1 - $9.23 1 - $10.95 1 - $6.60 3 - $7.92 1 - $9.24 2 - $11.00 1 - $6.63 1 - $8.00 1 - $9.27 1 - $11.07 1 - $6.65 1 - $8.01 2 - $9.35 1 - $11.13 1 - $6.72 1 - $8.03 3 - $9.36 1 - $11.16 2 - $6.75 5 - $8.10 1 - $9.38 1 - $11.22 1 - $6.78 1 - $8.12 5 - $9.45 2 - $11.25 1 - $6.80 1 - $8.16 2 - $9.48 2 - $11.27 2 - $6.84 2 - $8.19 1 - $9.54 1 - $11.30 1 - $6.86 1 - $8.22 1 - $9.57 1 - $11.36 1 - $6.89 1 - $8.25 1 - $9.59 1 - $11.40 2 - $6.93 3 - $8.28 2 - $9.60 2 - $11.43 1 - $7.02 3 - $8.33 1 - $9.62 2 - $11.52 1 - $7.05 1 - $8.36 2 - $9.63 2 - $11.55 2 - $7.07 1 - $8.37 1 - $9.66 2 - $11.61 1 - $7.08 2 - $8.40 1 - $9.68 1 - $11.69 1 - $7.11 1 - $8.45 2 - $9.69 1 - $11.70 1 - $7.13 2 - $8.46 1 - $9.78 1 - $11.88 2 - $7.14 1 - $8.52 2 - $9.80 1 - $11.90 3 - $7.20 5 - $8.55 1 - $9.81 1 - $11.99 1 - $7.25 1 - $8.60 1 - $9.87 1 - $12.06 1 - $7.26 4 - $8.64 4 - $9.90 1 - $12.15 2 - $7.28 1 - $8.67 1 - $9.92 1 - $12.18 1 - $7.29 1 - $8.69 2 - $9.99 1 - $12.24 3 - $7.35 1 - $8.73 1 - $10.01 1 - $12.30 1 - $7.37 2 - $8.75 1 - $10.05 1 - $12.32 1 - $7.47 1 - $8.76 2 - $10.08 1 - $12.35 1 - $7.50 1 - $8.78 1 - $10.17 2 - $12.42 1 - $7.52 5 - $8.82 1 - $10.20 1 - $12.51 4 - $7.56 1 - $8.85 2 - $10.26 1 - $12.65 1 - $7.62 1 - $8.88 3 - $10.29 2 - $12.69 4 - $7.65 2 - $8.91 3 - $10.35 1 - $12.75 1 - $7.67 1 - $8.94 2 - $10.44 1 - $12.92 2 - $7.70 1 - $8.96 1 - $10.53 1 - $12.96 3 - $7.74 3 - $9.00 1 - $10.56 1 - $13.23 1 - $7.77 1 - $9.02 1 - $10.64 1 - $13.41 1 - $7.79 2 - $9.03 2 - $10.71 1 - $13.56 2 - $7.80 1 - $9.12 3 - $10.80 1 - $14.49 1 - $7.82 2 - $9.18 1 - $10.85 1 - $15.18 There are plenty of solutions for five summands. Here are a few: $8.28 -- at least two solutions $8.47 -- at least two solutions $8.82 -- at least two solutions -- Mark Johnson mark@microunity.com (408) 734-8100 There may be many approximate solutions, for example: $1.01, $1.15, $2.41, and $2.54. These sum to $7.11 but the product is 7.1100061.
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