rosalyn works no more than 25 hours a week during the school year. she is paid $12 an hour for tutoring geometry and $8 an hour for delivering pizzas for Pizza King. she wants to spend at least 2 hours but no more than 7 hours a week tutoring. find rosalyns maximum earnings.
Shade the regions defined by
t+p <= 25
t >= 2
t <= 7
Find the vertices of the shaded regions, and evaluate
e = 12t + 8p
and pick the maximum
To find Rosalyn's maximum earnings, we need to determine how many hours she can spend delivering pizzas while also tutoring between 2 and 7 hours a week.
Since Rosalyn works no more than 25 hours a week during the school year, we know that the maximum number of hours she can spend tutoring and delivering pizzas combined is 25 hours.
Let's start by considering the minimum amount of time she spends tutoring, which is 2 hours. In this case, the maximum time she can spend delivering pizzas is 25 - 2 = 23 hours.
Now, let's calculate the maximum earnings from tutoring. Rosalyn is paid $12 per hour for tutoring geometry, so her earnings from tutoring can be calculated as: Earnings from tutoring = 2 hours * $12/hour = $24.
Next, let's calculate the maximum earnings from delivering pizzas. Rosalyn is paid $8 per hour for delivering pizzas, so her earnings from delivering pizzas can be calculated as: Earnings from delivering pizzas = 23 hours * $8/hour = $184.
Finally, let's find the maximum earnings by adding the earnings from tutoring and delivering pizzas:
Total Maximum earnings = Earnings from tutoring + Earnings from delivering pizzas = $24 + $184 = $208.
Therefore, Rosalyn's maximum earnings would be $208.