Question 138710
1)



The profit function is defined by:


Profit = Revenue - Cost




So in function notation it looks like:


{{{P(x)=R(x)-C(x)}}}



So in our case:


{{{P(x)=10x-(4x+170)}}} Plug in {{{R(x)=10x}}} and {{{C(x)=4x+170}}}



{{{P(x)=10x-4x-170}}} Distribute the negative



{{{P(x)=6x-170}}} Combine like terms



{{{6x-170>0}}} Set the right side greater than zero. Remember we're looking for positive profit.



{{{6x>170}}} Add 170 to both sides



{{{x>170/6}}} Divide both sides by 6



{{{x>28.333}}} Divide 



{{{x>29}}} Round to the nearest whole number. A third of a hammer can't be sold.




So when {{{x>29}}}, we'll have positive profit. So more than 29 hammers must be sold to gain a profit.




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2)


We're still using the profit function. So {{{P(x)=6x-170}}}



Since we want a profit of $100, simply plug in {{{P(x)=100}}}.



{{{P(x)=6x-170}}} Start with the profit function



{{{100=6x-170}}} Plug in {{{P(x)=100}}}



{{{270=6x}}} Add 170 to both sides



{{{45=x}}} Divide both sides by 6



So when {{{x=45}}}, we'll have a profit of $100. So 45 must be sold to make a profit of $100.