Question

An online company sells handmade samurai katana swords. The website costs $ 215 a month to maintain. Each katana costs $ 145 to make, and they sell each katana for $ 575.

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 $ 2350.

Answer 1

SOLUTION:

From given data,

An online company sells handmade samurai katana swords. The website costs $ 215 a month to maintain. Each katana costs $ 145 to make, and they sell each katana for $ 575.

given that,

The website costs $ 215 a month to maintain

Each katana costs $ 145 to make

they sell each katana for $ 575

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

Sale price of each katana = $575

Cost of making each katana=$145

Contribution from each katana sold= 575-145 = $430

Assume the fixed cost is $215=y₀ a month ,and x units sold a month,

Profit =y

So, Profit = no of units sold*430- 215

Or, y=x*430-215

Or y=430 x-y₀

Therefore the linear equation is y=430 x - 215

B. Using this model, find the number of swords that would need to be sold per month to have a monthly profit of $ 2350.

for y =2350 , the equation will be ,

2350  = 430 x - 215

2350 + 215 = 430 x

x = 2565 / 430

x = 5.96

Or 6 approx.

Therefore 5.96 or 6 katanas to be sold each month to have $ 2350 profit per month.