Given the cost function C(x)=0.85x+35,000?(?)=0.85?+35,000 and the revenue funct

Given the cost function C(x)=0.85x+35,000?(?)=0.85?+35,000 and the revenue funct

Given the cost function C(x)=0.85x+35,000?(?)=0.85?+35,000 and the revenue function R(x)=1.55x,?(?)=1.55?, the break-even point is (50,000,77,500) and the profit function is P(x)=0.7x−35,000.
Solution
Write the system of equations using y? to replace function notation.
y=0.85x+35,000y=1.55x?=0.85?+35,000?=1.55?
Substitute the expression 0.85x+35,0000.85?+35,000 from the first equation into the second equation and solve for x.?.
0.85x+35,000=1.55×35,000=0.7×50,000=x0.85?+35,000=1.55?35,000=0.7?50,000=?
Then, we substitute x=50,000?=50,000 into either the cost function or the revenue function.
1.55(50,000)=77,5001.55(50,000)=77,500
The break-even point is (50,000,77,500).(50,000,77,500).
The profit function is found using the formula P(x)=R(x)−C(x).?(?)=?(?)−?(?).
P(x)=1.55x−(0.85x+35,000)       =0.7x−35,000?(?)=1.55?−(0.85?+35,000)       =0.7?−35,000
The profit function is P(x)=0.7x−35,000.
The cost to produce 50,000 units is \$77,500, and the revenue from the sales of 50,000 units is also \$77,500. To make a profit, the business must produce and sell more than 50,000 units.
Assignment
1. Use the GeoGebra.com tool to graph the cost and revenue functions
2. Identify the break-even point using the “Intersect” tool under “Points” on GeoGebra
3. Save your GeoGebra work as a .pdf file for submission
Discuss the part of the graph that represents the profit.
Discuss how you found the break-even point on the graph.
If you are performing a break-even analysis for a business and their cost and revenue equations are dependent, explain what this means for the company’s profit margins.
If you are solving a break-even analysis and get more than one break-even point, explain what this signifies for the company?
If you are solving a break-even analysis and there is no break-even point, explain what this means for the company.
How should they ensure there is a break-even point?
Solve the following problem: An investor earned triple the profits of what she earned last year. If she made \$500,000.48 total for both years, how much did she earn in profits each year?
Write an analysis of your solution to this problem.
Describe the graph that could model this situation.