# Music Store

### Christian Basa

My business makes guitars and basses. Customers can buy either a guitar or bass.

# Restrictions

I can only make 300 guitars a month and only 150 basses per month. Guitars cost \$150 to make and sell for \$260. Basses cost \$175 to make and sell for \$250. I make a \$110 profit off of guitars and a \$75 profit off of basses. The production of these instruments cannot cost more than \$10,000 to make and no more than 3/4 of the \$10,000 can be spent on the production of only one type of instrument. In my beginning phase I can't spend more than \$8,000 a month.

# System of Inequalities

x=# of guitars

y=# of basses

Profit Equations

Sell Price

260x+250y=S

Total Cost

150x+175y=C

Profit

(260x+250y)-(150x+175y)=p or (110x+75y)=p

Restrictions

x≥0

y≥0

x≤300

y≤150

300x+150y≤10000

# Profits

The profit is the selling price minus the cost
of production.
x = # guitars; y = # basses
Cost = 150x+175y=c
Sell = 260x + 250y
Profit = sell – cost
P=(260x + 250y) – (150x + 175y)=110x+75y=P

# Maximizing Profits

(0,0)-110(0)+75(0)=0

(33.67,66.67)-110(33.67)+75(66.67)=\$8,670.95

(0,66.7)-110(0)+75(66.7)=\$5,002.5

(26.67,0)-110(26.67)+75(0)=\$2,933.7

(0,53.33)-110(300)+75(150)=\$3,999.75

If I make about 34 guitars and 64 basses I will make a profit of \$670.95 per month