<u>Scenario 1</u>
It is given that on Albert's favorite shoe website, the prices for a pair of the shoes range from $80 to $180 and the delivery fee is one-twentieth of the price of the basketball shoes.
We know that Albert has $105 to spend on new basketball shoes.
From the above pieces of information we see that the minimum that Albert will have to spend is dollars.
Now, we know that Albert can spend a maximum of $105 including the delivery fee. Let the upper limit of the price of the shoe Albert can buy be . So, the upper limit of the domain can be found as:
dollars.
Thus, in the first scenario, the domain of the total cost function, f(c) will be [86.67,96.92].
<u>Scenario 2</u>
After receiving $42 from his friend, Albert's total buying power becomes $147. Albert can now buy a costlier pair of shoes.
Thus, the maximum that Albert can buy is again given by:
Solving this we get: dollars
The lower limit will remain the same as the lowest price point in the website is $80. Therefore, in the second scenario the domain is:
[86.67, 135.69]