SOLUTION: i. Use trial and error to find the quantity of tile sets per month that yields the highest profit.

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Question 121751: i. Use trial and error to find the quantity of tile sets per month that yields the highest profit.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
#1 i

Notice that in part g) we had a profit of $475 (which was the largest profit so far). So let's increase x until we find the highest profit.




Let's find the profit when 26 tiles are sold:


f%28x%29=-1x%5E2%2B56x-300 Start with the given function.


f%2826%29=-1%2826%29%5E2%2B56%2826%29-300 Plug in x=26. In other words, replace each x with 26.


f%2826%29=-1%28676%29%2B56%2826%29-300 Evaluate %2826%29%5E2 to get 676.


f%2826%29=-676%2B56%2826%29-300 Multiply -1 and 676 to get -676


f%2826%29=-676%2B1456-300 Multiply 56 and 26 to get 1456


f%2826%29=480 Now combine like terms


So the when 26 tiles are sold, the profit is $480


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Let's find the profit when 27 tiles are sold:


f%28x%29=-1x%5E2%2B56x-300 Start with the given function.


f%2827%29=-1%2827%29%5E2%2B56%2827%29-300 Plug in x=27. In other words, replace each x with 27.


f%2827%29=-1%28729%29%2B56%2827%29-300 Evaluate %2827%29%5E2 to get 729.


f%2827%29=-729%2B56%2827%29-300 Multiply -1 and 729 to get -729


f%2827%29=-729%2B1512-300 Multiply 56 and 27 to get 1512


f%2827%29=483 Now combine like terms


So the when 27 tiles are sold, the profit is $483


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Let's find the profit when 28 tiles are sold:


f%28x%29=-1x%5E2%2B56x-300 Start with the given function.


f%2828%29=-1%2828%29%5E2%2B56%2828%29-300 Plug in x=28. In other words, replace each x with 28.


f%2828%29=-1%28784%29%2B56%2828%29-300 Evaluate %2828%29%5E2 to get 784.


f%2828%29=-784%2B56%2828%29-300 Multiply -1 and 784 to get -784


f%2828%29=-784%2B1568-300 Multiply 56 and 28 to get 1568


f%2828%29=484 Now combine like terms


So the when 28 tiles are sold, the profit is $484


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Let's find the profit when 29 tiles are sold:



f%28x%29=-1x%5E2%2B56x-300 Start with the given function.


f%2829%29=-1%2829%29%5E2%2B56%2829%29-300 Plug in x=29. In other words, replace each x with 29.


f%2829%29=-1%28841%29%2B56%2829%29-300 Evaluate %2829%29%5E2 to get 841.


f%2829%29=-841%2B56%2829%29-300 Multiply -1 and 841 to get -841


f%2829%29=-841%2B1624-300 Multiply 56 and 29 to get 1624


f%2829%29=483 Now combine like terms



So the when 29 tiles are sold, the profit is $483




Notice how the profit is steadily increasing from x=26 to x=28. However, it starts to decrease after x=28. So this shows that the highest profit of $484 occurs when 28 tiles are sold.