Question 122219
a)


{{{f(x)=2.25x-7000}}} Start with the given function.



{{{f(2000)=2.25(2000)-7000}}} Plug in {{{x=2000}}}



{{{f(2000)=4500-7000}}} Multiply 2.25 and 2,000 to get 4,500



{{{f(2000)=-2500}}} Subtract 7,000 from 4,500 to get -2,500




So her profit is -2,500 dollars when she sells 2,000 units. In other words, she loses 2,500 dollars when she sells 2,000 units.




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b)




{{{f(x)=2.25x-7000}}} Start with the given function.



{{{f(2000)=2.25(5000)-7000}}} Plug in {{{x=5000}}}



{{{f(2000)=11250-7000}}} Multiply 2.25 and 5,000 to get 11,250



{{{f(2000)=4250}}} Subtract 7,000 from 11,250 to get 4,250




So her profit is 4250 dollars when she sells 5,000 units




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c)


What is the break-even point for sales? The break even point occurs when {{{f(x)=0}}}



{{{f(x)=2.25x-7000}}} Start with the given function.



{{{0=2.25x-7000}}} Replace {{{f(x)}}} with 0



{{{-2.25x=7000}}} Subtract 2.25x from both sides



{{{x=-7000/-2.25}}} Divide both sides by -2.25 



{{{x=3111.11}}} Divide



So if you round to the nearest whole number, you get 



{{{x=3111}}}



So the break-even point is when she sells about 3,111 units