Questions: Let p=19-sqrt(x) and C(x)=215+4x, where x is the number of garden hoses that can be sold at a price of p per unit and C(x) is the total cost (in dollars) of producing x garden hoses. (A) Express the revenue function in terms of x. (B) Graph the cost function and the revenue function in the same viewing window for 0 ≤ x ≤ 361. Use approximation techniques to find the break-even points. (A) R(x)=

Let p=19-sqrt(x) and C(x)=215+4x, where x is the number of garden hoses that can be sold at a price of p per unit and C(x) is the total cost (in dollars) of producing x garden hoses.
(A) Express the revenue function in terms of x.
(B) Graph the cost function and the revenue function in the same viewing window for 0 ≤ x ≤ 361. Use approximation techniques to find the break-even points.
(A) R(x)=

Transcript text: Let $p=19-\sqrt{x}$ and $C(x)=215+4 x$, where $x$ is the number of garden hoses that can be sold at a price of $\$ p$ per unit and $C(x)$ is the total cost (in dollars) of producing $x$ garden hoses. (A) Express the revenue function in terms of $x$. (B) Graph the cost function and the revenue function in the same viewing window for $0 \leq x \leq 361$. Use approximation techniques to find the break-even points. (A) $R(x)=$ $\square$

Solution

Solution Steps

Step 1: Express the revenue function in terms of $ x $

The revenue function $ R(x) $ is given by the product of the price per unit $ p $ and the number of units sold $ x $.

Given $ p = 19 - \sqrt{x} $, the revenue function $ R(x) $ is: \[ R(x) = x \cdot p = x \cdot (19 - \sqrt{x}) = 19x - x^{3/2} \]

Final Answer

\[ R(x) = 19x - x^{3/2} \]

{"axisType": 3, "coordSystem": {"xmin": 0, "xmax": 361, "ymin": 0, "ymax": 10000}, "commands": ["y = 215 + 4x", "y = 19x - x**(3/2)"], "latex_expressions": ["$C(x) = 215 + 4x$", "$R(x) = 19x - x^{3/2}$"]}

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