For each cost function C \left( x \right) and revenue function R \left( x \right), use technology to find the number of units x that must be sold to break even:
Consider the following phone plans:
GO SMALL plan: This plan has a \$30 monthly base charge and charges 90 cents per minute for all calls.
GO MEDIUM plan: This plan has a \$38 monthly base charge and then charges 70 cents per minute for all calls.
Complete the following table of values for various total monthly call times for the two plans:
| Call time (in minutes) | Total cost for GO SMALL plan | Total cost for GO MEDIUM plan |
|---|---|---|
| 30 | ||
| 40 | ||
| 50 | ||
| 60 |
Sketch the graph of the two plans on the same set of axes.
Find how many minutes of calls results in the same monthly bill for both plans.
The cost C of manufacturing toys is related to the number n of toys produced by the formula C = 900 + 5 n. The revenue R made from selling n toys is R = 8 n.
Complete the following table:
| Number of toys | Cost (in dollars) | Revenue (in dollars) |
|---|---|---|
| 250 | ||
| 300 | ||
| 350 | ||
| 400 |
Sketch the graphs of the cost and the revenue on the same set of axes.
How many toys need to be produced for revenue to equal cost?
What does the y value of this point of intersection mean?
This graph shows the cost C \left(x\right), the revenue R \left(x\right) and the profit P \left(x\right) from making and selling x units of a certain good. Each line has been labelled.
Match the function to its correct label:
P \left(x\right)
C \left(x\right)
R \left(x\right)
How many units must be sold to reach the break-even point?
The monthly cost C \left( x \right), revenue R \left( x \right) and profit P \left( x \right) functions for a car washing company are given below, where x represents the number of clients in a month:
Find the company's fixed cost when they have no clients.
How much does the company charge each client per month?
Use technology to solve for the value of x (the number of services provided) that allows them to break even.
\begin{aligned} C \left( x \right) &= 38 x + 1700 \\ R \left( x \right) &= 55 x \\ P \left( x \right) &= 17 x - 1700 \end{aligned}
State whether each statement is true for the following graphs:
The fixed cost for this venture is \$0.
There is no break-even point for this venture.
The cost per unit is less than the revenue per unit.
The fixed cost for this venture is \$0.
There is no break-even point for this venture.
Total revenue exceeds total cost after 9 units.
The two equations y = 5 x + 800 and y = 7 x represent the cost and revenue functions of Jim's Haberdashery respectively. The value of x is the number of clients he sees in a month.
Graph both equations on the same set of axes.
How much does each client cost Jim?
How much revenue does each client earn Jim?
What does the point \left(400, 2800\right) represent?
The cost for a sporting goods manufacturer to make bats is \$60 per bat plus a fixed setup cost of \$400. The bats will sell for \$85 each.
Write an equation in the form \\y = m x + b to represent the cost y of manufacturing x bats.
Write an equation in the form \\y = m x to represent the revenue y generated from the sale of x bats.
The two equations are plotted on the graph. Find the coordinates of the break-even point.
How many bats must be produced and sold for revenue to exactly cover the cost of production?
Find the cost of production at this point.
The graph shows the cost of producing drink bottles and the revenue from the sales of the drink bottles for a particular company:
Find the gradient and the y-intercept of the line representing the cost of producing the drink bottles.
Gradient
Find the equation of the line representing the cost of producing the drink bottles.
Find the quantity of bottles that needs to be sold to break even.
The cost for a furniture manufacturer to make an armchair is \$500 per armchair plus a fixed setup cost of \$3500. The armchairs will sell for \$650 each.
Write an expression to represent the cost of manufacturing x armchairs.
Write an expression to represent the revenue generated from the sale of x armchairs.
Find the break-even point.