Help with a few questions please?

[Noctirna]

Could someone help solve these math problems I'm having troubles with, and show me how you worked them out so I can understand how you did them, please? Thanks for your help


1. The revenue (in millions of dollars) from the sale of x units at a home supply outlet is given by R(x)=0.14x. The profit (in millions of dollars) from the sale of x units is given by P(x)=0.087x-0.7. Find the Cost equation and what is the break even point?


C(x)=____________


The break even points occurs when x=______ units are sold.


2. Rose makes and sells candy. She has found that the cost per box for making x boxes of candy is given by the following cost function.
C(x)=x^2-40x+247.


How many boxes should she make in order to keep the cost per box to a minimum? __________(round to the nearest whole number)


3. If a tennis ball is projected upward from the ground level with an initial velocity of 96 ft per second, then its height is a function of time: s=-16t^2+96t. What is the maximum height reached by the ball?__________

 

[Deleted member 4993]

Could someone help solve these math problems I'm having troubles with, and show me how you worked them out so I can understand how you did them, please? Thanks for your help


1. The revenue (in millions of dollars) from the sale of x units at a home supply outlet is given by R(x)=0.14x. The profit (in millions of dollars) from the sale of x units is given by P(x)=0.087x-0.7. Find the Cost equation and what is the break even point?

How would you express cost function [C(x)] in terms of Profit function [P(x)] and Revenue function [R(x)]?

Just think about it: You sold something for 8 bucks and you had purchased it for 5.50 bucks. How much profit did you make?

C(x)=____________


The break even points occurs when x=______ units are sold.


2. Rose makes and sells candy. She has found that the cost per box for making x boxes of candy is given by the following cost function.
C(x)=x^2-40x+247.


How many boxes should she make in order to keep the cost per box to a minimum? __________(round to the nearest whole number)


3. If a tennis ball is projected upward from the ground level with an initial velocity of 96 ft per second, then its height is a function of time: s=-16t^2+96t. What is the maximum height reached by the ball?__________

What are your thoughts?

Please share your work with us ...even if you know it is wrong.

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/announcement.php?f=33

 

[Noctirna]

That's just it I have no work to show because I am stuck at the beginning. I don't understand what is being asked. I don't get what is mean't be "In millions" either.

 

[Deleted member 4993]

That's just it I have no work to show because I am stuck at the beginning. I don't understand what is being asked. I don't get what is mean't be "In millions" either.

Okay - so for the first problem -


1. The revenue (in millions of dollars) from the sale of x units at a home supply outlet is given by R(x)=0.14x. The profit (in millions of dollars) from the sale of x units is given by P(x)=0.087x-0.7. Find the Cost equation and what is the break even point?

Search your classnotes or textbook or internet (like Google) and learn the definitions of:

1. The revenue
2. The profit
3. The Cost
   After that please come back and tell us the definitions of those terms.

 

[Noctirna]

1. Sales revenue is generated by multiplying the number of a product sold by the sales amount using the formula: Sales Revenue = Units Sold x Sales Price. The more sales a company makes, the more money available within the business.

2. The profit equation is used to determine a company's profitability and can be described in its simplest form as Profit = Sales minus Costs. "Costs" refers to a figure that reflects both fixed and variable costs combined. The figure for "sales" is derived by multiplying the number of units sold by their unit cost.

3. A cost equation is a mathematical formula that a company can use to predict the expenses associated with the production and sale of a certain amount of goods. The formula typically incorporates constant overhead costs as well as variable costs that depend on the volume of sales. To use the cost equation, companies input sales volume in place of the equation's variable and solve for the cost of production.

 

[Deleted member 4993]

1. Sales revenue is generated by multiplying the number of a product sold by the sales amount using the formula: Sales Revenue = Units Sold x Sales Price. The more sales a company makes, the more money available within the business.

2. The profit equation is used to determine a company's profitability and can be described in its simplest form as Profit = Sales minus Costs. "Costs" refers to a figure that reflects both fixed and variable costs combined. The figure for "sales" is derived by multiplying the number of units sold by their unit cost.

3. A cost equation is a mathematical formula that a company can use to predict the expenses associated with the production and sale of a certain amount of goods. The formula typically incorporates constant overhead costs as well as variable costs that depend on the volume of sales. To use the cost equation, companies input sales volume in place of the equation's variable and solve for the cost of production.

Great!

Now please tell us:

What is the mathematical relation between "revenue", "profit" and "cost" ?

 

[Otis]

If a tennis ball is projected upward from the ground level with an initial velocity of 96 ft per second, then its height is a function of time: s=-16t^2+96t. What is the maximum height reached by the ball?

They're using symbol s to represent the height. Do you recognize that s is defined by a quadratic polynomial?

In other words, the given formula takes the form y=ax^2+bx+c, and its graph is a downward-opening parabola. On this graph, the maximum height is at the parabola's vertex point.

There's a formula for finding the x-coordinate of the vertex point; it uses the coefficients a and b:

x-coordinate of vertex point = -b/(2a)

Once you've calculated that value, you can use it to find the corresponding y-coordinate (maximum height) by substitution into the formula for y.

Now, in your exercise, they're using different variable names (t for x, and s for y), but the pattern is the same.

(1) t-coordinate of vertex point = -b/(2a)

(2) substitute the result for t into s=-16t^2+96t, to obtain the corresponding height.

If none of this seems familiar, or you're feeling quite lost, ask your school if they have tutoring resources for face-to-face sessions.

Otherwise, give it a try, and post your work here if there are questions. Cheers :cool:

 

[Otis]

I don't get what is meant by "In millions"

That tells us the units, on the dollar amounts.

For example, if they sold ten items, then their revenue is

R(10) = 1.4

The output 1.4 does not represent $1.40 because "in millions" means a million times more.

In other words, 1.4 means $1,400,000, in this exercise.

Same goes for profit.

P(10) = 0.17

That's a profit of $170,000.

The benefit of using units like this is to keep formulas concise. If they did not report "in millions", then the formulas for revenue and profit would need to be

R(x) = 140000x

P(x) = 87000x - 700000

Questions? :cool: