First week sells 6 chairs for $80 each. Next week, if chair is not sold, it will sell for 0.85 times previous week's price. Store needs to sell 6 chairs for total of $270 to make a profit. what is the last week in which all 6 chairs could be sold so that the store makes a profit?
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To find the last week in which all 6 chairs can be sold and the store makes a profit, we'll need to follow the given conditions.
Let's start by calculating the price of chairs in each subsequent week.
First week: 6 chairs sold at $80 each, so the total revenue is 6 * $80 = $480.
Next week: If the chair is not sold, it will be sold for 0.85 times the previous week's price. Therefore, the price in the second week would be 0.85 * $80 = $68.
Now, let's find the revenue in the second week when all 6 chairs are sold at $68 each:
Second week: 6 chairs sold at $68 each, so the total revenue is 6 * $68 = $408.
We can see that the revenue in the second week is less than the revenue in the first week. So, let's continue with the calculation for the subsequent weeks.
Third week: The price of chairs would be 0.85 times the price in the second week: 0.85 * $68 = $57.80.
Third week revenue: 6 chairs sold at $57.80 each, so the total revenue is 6 * $57.80 = $346.80.
Fourth week: The price of chairs would be 0.85 times the price in the third week: 0.85 * $57.80 ≈ $49.23
Fourth week revenue: 6 chairs sold at $49.23 each, so the total revenue is 6 * $49.23 = $295.38.
Fifth week: The price of chairs would be 0.85 times the price in the fourth week: 0.85 * $49.23 ≈ $41.85.
Fifth week revenue: 6 chairs sold at $41.85 each, so the total revenue is 6 * $41.85 = $251.10.
Now, we can see that the revenue in the fifth week is less than the desired profit of $270. Therefore, the last week in which all 6 chairs could be sold so that the store makes a profit is the fourth week.
In summary, the answer is the fourth week.