(a) The cost C as a function of x is given by:
C(x) = 2500 + 4x
The initial start-up cost is $2500 and it costs him $4 per delivery.
(b) The revenue R as a function of x is given by:
R(x) = 6.50x
He charges $6.50 per delivery, so the revenue is simply the price per delivery multiplied by the number of deliveries.
(c) To determine the value of x for which revenue equals cost, we need to set C(x) equal to R(x) and solve for x:
2500 + 4x = 6.50x
2500 = 2.50x
x = 2500/2.50
x = 1000
So when he makes 1000 deliveries, the revenue will equal the cost.
(d) The graph of the equations y = C(x) and y = R(x) on the same axes will have x as the independent variable on the x-axis and the cost and revenue on the y-axis. The graph will be a linear function with a positive slope.
The graph will start at C = 2500 on the y-axis at x = 0, indicating the initial start-up cost. As the number of deliveries (x) increases, the cost (y) will increase at a rate of $4 per delivery. The revenue (y) will increase at a rate of $6.50 per delivery, starting from the origin.
The point of intersection of the two graphs represents the number of deliveries (x) at which the revenue equals the cost. In this case, it is x = 1000.
A person operates a delivery service in a southern city. His start-up costs amounted to $2500. He estimates that it costs him (in terms of gasoline, wear and tear on his car, etc.) $4.00 per delivery. He charges $6.50 per delivery. Let x represent the number of deliveries he makes.
(a) Express the cost C as a function of x, where x represents the quantity of items as given.
(b) Express the revenue R as a function of x.
(c) Determine the value of x for which revenue equals cost.
(d) Graph the equations y=C(x) and y=R(x) on the same axes, and interpret the graph.
1 answer
1 answer