can you help me with these questions?
A hair stylist rents a chair at an independent salon for the price of 500 dollars per week
and additionally pays 15 percent of revenue back to the salon. Suppose that the hair
stylist's average revenue is 120 dollars per client.
1.what is the profit function?
2.what is the break- even point. What is the minimum number of clients required in a given week to produce a profit?
3. how many clients must the hair stylist serve to make a 200 percent profit?
many thanks.
math questions........?
2016-08-18 5:57 am
回答 (2)
2016-08-18 6:17 am
let
x = number of clients
P = 120x - .15 * 120x - 500
P = 120x - 18x - 500
P = 102x - 500
break even point is when P = 0
0 = 102x - 500
500 = 102x
4.9019607843137254901960784313725 = x
4.9 clients is the break even point
since you can't have .9 of a client
the stylist needs at least 5 clients
P = 102 * 5 - 500
P = 10
the stylist makes a profit of $10 with 5 clients
the 200% doesn't make sense.
if the stylist wants a profit of at least $200
200 = 102x - 500
700 = 102x
6.8627450980392156862745098039216 = x
the stylist needs at least 7 clients to make at least $200
x = number of clients
P = 120x - .15 * 120x - 500
P = 120x - 18x - 500
P = 102x - 500
break even point is when P = 0
0 = 102x - 500
500 = 102x
4.9019607843137254901960784313725 = x
4.9 clients is the break even point
since you can't have .9 of a client
the stylist needs at least 5 clients
P = 102 * 5 - 500
P = 10
the stylist makes a profit of $10 with 5 clients
the 200% doesn't make sense.
if the stylist wants a profit of at least $200
200 = 102x - 500
700 = 102x
6.8627450980392156862745098039216 = x
the stylist needs at least 7 clients to make at least $200
2016-08-18 6:03 am
1. I'm not entirely sure what is meant by profit function, but a function of her total income is this
income = 120x - 0.15(120x) - 500
2. The break even point is the point of intersection of the two equations. Notice that they are both linear equations. To find the point of intersection, we simply set the two equal to each other, and solve for the number of clients necessary to break even:
500 + 0.15(120x) = 120x
Solve for x.
3. To calculate the amount of clients needed for 200 percent profit, you need to solve the equation
(2)(500 + 0.15(120x)) = (120x)
where the left side is multiplied by 2, because you want to know when her profit is equal to twice her expenses.
income = 120x - 0.15(120x) - 500
2. The break even point is the point of intersection of the two equations. Notice that they are both linear equations. To find the point of intersection, we simply set the two equal to each other, and solve for the number of clients necessary to break even:
500 + 0.15(120x) = 120x
Solve for x.
3. To calculate the amount of clients needed for 200 percent profit, you need to solve the equation
(2)(500 + 0.15(120x)) = (120x)
where the left side is multiplied by 2, because you want to know when her profit is equal to twice her expenses.
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