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A truck driver 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​ truck, etc.)​$3.00 per delivery. He charges ​$5.50 per delivery. Let x represent the number of deliveries he makes. ​(a) Express the cost C as a function of x. ​(b) Express the revenue R as a function of x. ​(c) Determine analytically the value of x for which revenue equals cost. ​(d) Graph y1equals​C(x) and y2equals​R(x) on the same​ xy-axes and interpret the graphs.

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MechEngineer

Answer:

(a)C(x) = 2500 + 3x

(b)R(x) = 5.5x

(c)x = 1000

Step-by-step explanation:

(a)His cost function as a function of x

C(x) = 2500 + 3x

(b)His revenue R function as a function of x

R(x) = 5.5x

(c)When revenue R equals to Cost C

C(x) = R(x)

2500 + 3x = 5.5x

2.5x = 2500

x = 1000

(d) Refer to attachment. We can see that the 2 lines intercepts at x = 1000 and y = 2500. That's the point of turning to profit.

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