SOLUTION: The cost of producing a number of items x is given by C = mx + b, in which b is the fixed cost and m is the variable cost (the cost of producing one more item). (a) If the fixed c

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The cost of producing a number of items x is given by C = mx + b, in which b is the fixed cost and m is the variable cost (the cost of producing one more item). (a) If the fixed c      Log On


   

Question 60915This question is from textbook
: The cost of producing a number of items x is given by C = mx + b, in which b is the fixed cost and m is the variable cost (the cost of producing one more item).
(a) If the fixed cost is $40 and the variable cost is $10, write the cost equation.
(b) Graph the cost equation.
(c) The revenue generated from the sale of x items is given by R = 50x. Graph the revenue equation on the same set of axes as the cost equation.
(d) How many items must be produced for the revenue to equal the cost (the break-even point)? This question is from textbook

Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
The cost of producing a number of items x is given by C = mx + b, in which b is the fixed cost and m is the variable cost (the cost of producing one more item).
(a) If the fixed cost is $40 and the variable cost is $10, write the cost equation.
b=40, m=10
highlight%28C=10x%2B40%29
(b) Graph the cost equation.
graph%28300%2C200%2C-10%2C10%2C-10%2C50%2C10x%2B40%29
(c) The revenue generated from the sale of x items is given by R = 50x. Graph the revenue equation on the same set of axes as the cost equation.
graph%28300%2C200%2C-10%2C10%2C-10%2C60%2C10x%2B40%2C50x%29
(d) How many items must be produced for the revenue to equal the cost (the break-even point)? The lines intersect at (1,50), therefore the number of items that must be produced to break even is x=1.
You could have found this algebraically by letting C=R
10x+40=50x
10x-10x+40=50x-10x
40=40x
40/40=40x/40
1=x
Happy Calculating!!!