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

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) (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:

Start with the given function.

Plug in . In other words, replace each x with 26.

Evaluate to get 676.

Multiply -1 and 676 to get -676

Multiply 56 and 26 to get 1456

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:

Start with the given function.

Plug in . In other words, replace each x with 27.

Evaluate to get 729.

Multiply -1 and 729 to get -729

Multiply 56 and 27 to get 1512

Now combine like terms

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

------------------------------------------------

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

Start with the given function.

Plug in . In other words, replace each x with 28.

Evaluate to get 784.

Multiply -1 and 784 to get -784

Multiply 56 and 28 to get 1568

Now combine like terms

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

------------------------------------------------

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

Start with the given function.

Plug in . In other words, replace each x with 29.

Evaluate to get 841.

Multiply -1 and 841 to get -841

Multiply 56 and 29 to get 1624

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.

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