<PRE><B>Question 293503</B>
d = 600 - 40p
d is the number of cans
p is the price per can


When p = 5, d = 600 - 40*5 = 600 - 200 = 400 cans per week.


When p = 6, d = 600 - 40*6 = 600 - 240 = 360 cans per week.


When p = 7, d = 600 - 40*7 = 600 - 280 = 320 cans per week.


Every dollar increase in the price means 40 less cans sold per week.


Your questions are:


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a)Will Helen sell more or less Muscle Punch if she raises her price from $5?


She will sell less punch.


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b)What happens to her sales every time she raises her price by $1?


She sells 40 less cans per week.


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c)Graph the equation.


To graph this equation, change d to y and change p to x.
Your equation becomes y = 600 - 40*x
Graph of your equation looks like this:
{{{graph(400,400,-5,20,-100,900,600-40x,600)}}}


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d)What is the maximum price that she can charge and still sell at least one can?


From the graph, it&#39;s clear that when she sells at $15.00 per can, she will not sell any cans.


From the formula, this becomes d = 600 - 40*15 = 600 - 600 = 0


As long as the price is less than $15.00 per can, she will sell something, even if it&#39;s just part of a can.


Since she can&#39;t really sell part of a can, the smallest increment she can sell is 1 can.


We can figure out what the highest price has to be in order for her to sell 1 can.


The formula is:


d = 600 - 40*p


We set d = 1 to get:


1 = 600 - 40*p


We subtract 1 from both sides of this equation and we add 40*p to both sides of this equation to get:


40*p = 599


We divide both sides of this equation by 40 to get:


p = 599/40 = $14.975 per can.


At that price, she will sell 1 can.


That&#39;s the highest price she can sell each can for and still be able to sell at least 1 can based on the formula.


Her price must be less than or equal to $14.975 in order for her to sell at least 1 can.


That&#39;s the answer to question d.


The rest is just additional information.


Continue reading only if interested.


It appears that the differential price per can is equal to $15.00 - $14.975 = $.025.


This means that if she drops the price by another $.025, she should be able to sell exactly 1 more can.


To see if that works, we put that into the formula.


The formula is d = 600 - 40*p


We set p = $14.975 and we get d = 600 - 40*14.975 = 600 - 599 = 1


We set p = $14.950 and we get d = 600 - 40*14.950 = 600 - 598 = 2


The increment for selling exactly 1 more or less cans is equal to $.025 per can.


That makes sense because in the formula d = 600 - 40*p, if we just look at the 40*p part, we see that 40*.025 = 1, 40*.05 = 2, etc.


Your answer to question d is that the maximum price per can in order for her to sell at least 1 can is $14.975 per can.


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