# Pre-Calculus

posted by Erica

The monthly revenue acheived by selling x boxes of candy is calculated to be x(5-0.05x)dollars. The wholesale cost of each box of candy is \$1.50. How many boxes must be sold each month to achieve a profit of at least \$60.
Can someone please let me know how to set up this equation. I have looked everywhere for help.

You have to define three functions: the revenue function R(x), the cost function C(x) and the profit function P(x)=R(x) - C(x)
We're told R(x)=x(5-0.05x) and C(x)=1.50*x
Thus P(x)=R(x)-C(x)=x(5-0.05x) - 1.50*x
So you want to solve for x when P(x)=60 or
60=x(5-0.05x) - 1.50*x
This is a quadratic equation so be sure to use only positive roots. You might want to graph P(x) to see what it looks like and to see when it starts to fall below 60 because of decreasing marginal profitability.

Net x = the number of boxes sold

Profit = Revenue - Cost = 60

x(5-0.05x) - 1.5 x = 60

3.5 x - .05 x^2 = 60
which can be rewritten
x^2 - 70 x + 1200 = 0

That quadratic equation will have two roots.
Take the lowest positive root.

## Similar Questions

1. ### PreCalc

The monthly revenue achieved by selling x wristwatches is figured to be x(40-0.2x)dollars. The wholesale cost of each watch is \$32. a. How many watches need to be sold each month to achieve a profit (revenue-cost) of \$50?
2. ### Algebra

1. In this problem, we will analyze the profit found for sales of a certain product. A demand equation (sometimes called a demand curve) shows how much money people would pay for a product depending on how much of that product is available …
3. ### Algebra

. In this problem, we will analyze the profit found for sales of a certain product. A demand equation (sometimes called a demand curve) shows how much money people would pay for a product depending on how much of that product is available …
4. ### calculus

A candy company needs a custom box for their truffles. The box they've chose is in the shape of a cylinder with a hemisphere of the same radius on top. The total volume of the box is V= (1/2) ((4pir^2)/(3))+ pir^2 (y-r), where y is …
5. ### Math

A confectioner perchased several boxes of candy for \$6. He gave five boxes to his children, and sold the rest at 10 cents more per box than he had paid for them, and made a profit of 25% on his original cost. How much did a box of …

Caleb sold boxes of candy. Some sold for \$2, and some sold for \$3. He sold a total of 35 boxes and received \$92. How many boxes did he sell for \$2?
7. ### Pre-Algebra

Write a linear system of equations that can be used to solve these problems. Then, solve to get your final answer. Please help me work through this. 4. The difference of two numbers is 3. Their sum is 13. Find the numbers. 5. Matt …
8. ### math

A profit function is derived from the production cost and revenue function for a given item. The monthly profit function for a certain item is given by P(x)=−0.05x^2+400x−100,000, where P is in dollars and x is the number …
9. ### Math

Robin and Emily are selling boxes of candy bars. Robin sells 36 boxes of candy and Emily sells 24 boxes of candy. Which expression, using the form a(b+c), represents the amount they sold together a. 2(12+24) b. 4(9+6) c. 24 (6 + 36) …
10. ### Math

Robin and Emily are selling boxes of candy bars. Robin sells 36 boxes of candy and Emily sells 24 boxes of candy. Which expression, using the form a(b+c), represents the amount they sold altogether?

More Similar Questions