# The Dance Chamber

### Trystan Brown4/21/15

My business is The Dance Chamber dance lessons. I will be providing two styles of dance lessons, Ballet and Jazz to anyone who is interested in learning how dance. The dance lessons will be sold monthly. There will be one ballet and one jazz class a week.

# Restrictions

I can only teach a total of 8 class per month, 4 Ballet and 4 Jazz and I have a budget of \$700 per month. The ballet class will be sold for \$50 per class and jazz will be sold for \$25 per class. It cost \$10 to prepare for ballet lessons and \$5 to prepare for jazz lessons.

# System of inequalities

x= # of ballet classes

y= # of Jazz classes

Profit equation:

Sell

50x + 25y = S

Cost

10x + 5y = C

Profit

40x + 20y = P

Restrictions:

x ≥ 0

y ≥ 0

x ≤ 4

y ≤ 4

10x + 5y ≤ 700

# Maximizing Profit

Profit:

40x + 20y = P

Vertices of Feasible Region:

(0,4), (4,4), (4,0)

40(0) + 20(4) = \$80

40(4) + 20(4) = \$240

40(4) + 20(0) = \$160

# Conclusion

To make to most profit I should sell 4 ballet classes and 4 jazz classes a month and make \$240 per person who takes the classes.