Problema Solution
Given the cost and revenue functions (in dollars) for a frozen-yogurt shop
C (x)=400x+400 over x+4 (fraction)
R (x) =100x
(a) Define "break-even point" and find the break-even point from the above cost function.
(b)Define "profit function" and find the Profit Function
(c)Explain if P(4) represents a profit or a loss
Answer provided by our tutors
(a) Define "break-even point" and find the break-even point from the above cost function.
"break-even point" is the point at which cost or expenses and revenue are equal: there is no net loss or gain
C(x) = R(x)
(400x + 400)/(x + 4) = 100x
x = 2
click here to see the step y step solution of the equation
it is shown graphically as the point where the total revenue and total cost curves meet
click here to see the graph
(b) Define "profit function" and find the Profit Function
Profit function P(x) is the difference between total sales revenues R(x) and total costs C(x):
P(x) = R(x) - C(x)
P(x) = 100x - (400x + 400)/(x + 4)
P(x) = 100(x - 2)(x + 2)/(x + 4)
(c) Explain if P(4) represents a profit or a loss
P(4) = 100(4 - 2)(4 + 2)/(4 + 4)
P(4) = 100*2*6/8
P(4) = $150
Since P(4) > 0 follows P(4) represents profit of $150.