Question

A company produces accessories for smart phones and tablets. The profit on each smart phone case is $2, and the profit on each tablet case is $3. The company made a profit of $1,200 on the cases last month. The equation 2x + 3y = 1,200 represents the company's profit from cases last month, where x is the number of smart phone cases sold and y is the number of tablet cases sold. The function notation is f(x)=-2/3x+400. What would the graph for the function notation represent?

Answer 1

this is simple

Answer 2

@triciaal Please help! I will be back on about 30 mins.

Answer 3

ok

Answer 4

\(\bf 2x+3y=1200\qquad y=f(x)\qquad thus
\\ \quad \\
2x+3f(x)=1200\implies 3f(x)=-2x+1200\implies f(x)=\cfrac{-2x+1200}{3}
\\ \quad \\
f(x)={\color{brown}{-\cfrac{2}{3}}}x+400\impliedby {\color{brown}{ slope\implies rate\ of\ change}}\)

keep in mind that, that's the rate of change of "y" as "x" fluctuates
so if say x = 0
then -2/3 x = 0
and -2/3x + 400 = 0 + 400

that means, that if you produce NO smartphone cases, x = 0, then you'd be able to produce 400 tablet cases and show a profit of 1,200

the more smartphone cases you'd produce, would decrease the tablet cases you can produce, at that rate
staying within the 1,200 constaint

Answer 5

@awesomeness_dude I still dont get what the answer to my question is

Answer 6

@DanJS

Answer 7

@jim_thompson5910

Answer 8

@morganvaughn the question is:

The function notation is f(x)=-2/3x+400. What would the graph for the function notation represent?

y = number of tablet cases
x = number of phone cases

f() = y so the equation is like saying

\( y = -\frac{2}{3}x + 400 \)

x is the number of phones cases so if we input 0 for x that means y = 400 and we can sell 400 tables cases and still make a profit of 1,200. If x = 3 that means we sold three phone cases and y would equal 398, which means if we sell 3 phone cases we should not sell / produce more than 398 tables cases to stay at within 1,200 profit.

Answer 9

so @MDoodler is "x is the number of phones cases so if we input 0 for x that means y = 400 and we can sell 400 tables cases and still make a profit of 1,200. If x = 3 that means we sold three phone cases and y would equal 398, which means if we sell 3 phone cases we should not sell / produce more than 398 tables cases to stay at within 1,200 profit." the answer or you explaining?

Answer 10

I get it. Thank you!