Question

An online company sells handmade samurai katana swords. The website costs $ 390 a month to maintain. Each katana costs $ 195 to make, and they sell each katana for $ 695. A. Create a linear model in the form y=mx+yoy=mx+yo where xx is the number of swords sold per month and yy 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 $ 2090.

Answer 1

The correct answer is the linear model would be y = 500x - 390 where x is the number of swords sold in a month and y is the net monthly profit; B. 4.96 ≈ 5 swords monthly.

Explanation:

Let x number of swords are sold per month.

Cost price of the swords per month is $ 195x.

Fixed cost to maintain the website per month is $390.

Total cost incurred per month is $ (195x + 390).

Selling price per katana is $695.

Total selling price of x swords per month is $695x.

Therefore, Net monthly profit y =695x - (195x + 390)

⇒ y = 695x - 195x - 390

⇒ y = 500x - 390

Thus the linear model would look like y = 500x - 390 where x is the number of swords sold in a month and y is the net monthly profit.

B. Now, given monthly profit y = $2090.

Thus the number of swords needed to be sold is

2090 = 500x - 390

⇒ 2480 = 500x

⇒ x = 4.96

A minimum of 5 swords need to be sold to get a monthly profit of more than $2090.