Question

Please Show Work!

An online company sells handmade samurai katana swords. The website costs $ 175 a month to maintain. Each katana costs $ 265 to make, and they sell each katana for $ 705.

A. Create a linear model in the form ?=??+??y=mx+yo where ?x is the number of swords sold per month and ?y is the net monthly profit.


B. Using this model, find the number of swords that would need to be sold per month to have a monthly profit of $ 3100.

Answer 1

A.

Revenue per unit R(x)= $705

Variable cost per unit= $265

Fixed cost = $175

Net monthly profit= (revenue per unit- variable cost per unit) – fixed cost

Let,

Y = Net monthly income

X= Number of units sold per month

Therefore, the equation is

Y= (705X – 265X)- 175

Y= 440X – 175

B.

Y = 440X – 175

Here, Y = $3100

Therefore,

$3100 = 440X – 175

$3100+ $175 = 440X

440x = $3275

X= $3275/440

X = 7.443

The number of swords to be sold in order to produce a profit of $3100 is 7.443 units.