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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.
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.
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