Question

Right moves dance academy wishes to run two dance courses - Hip-hop and Contemporary. Fee for Hip-hop is \[Rs.300\] per hour and for contemporary it is $ Rs.250 $ per hour. The academy can accommodate at most $ 15 $ in hip-hop and at most $ 20 $ in contemporary. If the total number of students cannot exceed $ 30 $ , find the maximum revenue academy can get per hour.​

Answer 1

Hint: First we have to define what the terms we need to solve the problem are.
Since we have to find the total revenue of the classes per hour, write the income from hip-hop and contemporary in terms of unknown variables for students and add them.

Complete step by step answer:
Since from the given problem, Fee for hip-hop is \[Rs.300\] per hour. For contemporary it is $ Rs.250 $ per hour. Maximum students allowed for hip-hop = $ 15 $ , maximum students allowed for contemporary = $ 20 $ and total number of students allowed per hour = $ 30 $ .
By given let the number of students accepted for hip-hop so that the revenue is higher per hour be $ x $
And maximum number admitted is $ 30 $ , therefore accepted revenue is $ 30 - x $ students
Since for hip-hop the fee is $ 300 $ per student that means $ 300x $ rupees will pay.
Thus, the fee for contemporary is $ 250 $ per student. $ (30 - x) $ will pay $ 250(30 - x) $ rupees.
Therefore, the total revenue generated $ 300x + (30 - x)250 = 300x + 7500 - 250x $
Approaching further we get $ 50x + 7500 $ is the maximum revenue, since hip-hop allowed revenue is $ x = 15 $ , We get maximum revenue $ = 50x + 7500 = 50 \times 15 + 7500 = 8250 $
Thus, we get maximum revenue that can be generated by right classes per head is $ 8250 $ rupees.

Note: First write down the known values and then try to find the correct formula for it and then start to simplify further to find the unknown variables like this using the mathematical formulas. Since we have to find the total revenue of the classes per hour, write the income from hip-hop and contemporary in terms of unknown variables for students and add them.