Math Problem Statement

A company manufactures microchips. Use the revenue function ​R(x)equalsx left parenthesis 70 minus 5 x right parenthesis and the cost function ​C(x)equals121 plus 13 x to answer parts​ (A) through​ (D), where x is in millions of chips and​ R(x) and​ C(x) are in millions of dollars. Both functions have domain 1 less than or equals x less than or equals 20. Question content area bottom Part 1 ​(A) Form a profit function​ P, and graph​ R, C, and P in the same rectangular coordinate system. ​P(x)equals    negative 5 x squared plus 57 x minus 121 ​(Type your answer in standard​ form.) Part 2 Which graph below shows​ R(x), C(x), and​ P(x)? The​ blue, dashed curve represents​ R; the pink line represents​ C; and the​ green, solid curve represents P. A. 0 20 0 260 x y

A coordinate system has a horizontal x-axis labeled from 0 to 20 in increments of 2 and a vertical y-axis labeled from 0 to 260 in increments of 20. A line rises from left to right, passing through the y axis at y=120. A downward facing parabola that is dashed has x intercepts at x=1.6 and x=12.4 and a vertex at (7,150). A second downward facing parabola has x intercepts at x=2.8 and x=8.6 and a vertex at (5.7,40). All coordinates are approximate. B. 0 20 0 260 x y

A coordinate system has a horizontal x-axis labeled from 0 to 20 in increments of 2 and a vertical y-axis labeled from 0 to 260 in increments of 20. A line rises from left to right, passing through the y axis at y=120, intersecting a downward facing parabola at x=2.8 and x=8.6. This parabola is dashed and has x intercepts at x=0 and x=14 and a vertex at (5.7,250). A second downward facing parabola has x intercepts at x=0.4 and x=11 and a vertex at (5.7,140). All coordinates are approximate. C. 0 20 0 260 x y

A coordinate system has a horizontal x-axis labeled from 0 to 20 in increments of 2 and a vertical y-axis labeled from 0 to 260 in increments of 20. A line falls from left to right, passing through the y axis at y=120 and the x axis at x=9.3. A downward facing parabola that is dashed has x intercepts at x=0 and x=14 and a vertex at (5.7,250). A second downward facing parabola has x intercepts at x=2.8 and x=8.6 and a vertex at (5.7,40). All coordinates are approximate. D. 0 20 0 260 x y

Solution

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Math Problem Analysis

Mathematical Concepts

Quadratic Functions
Linear Functions
Profit Calculation
Graph Interpretation

Formulas

Profit function P(x) = R(x) - C(x)
Revenue function R(x) = 70x - 5x^2
Cost function C(x) = 121 + 13x

Theorems

Properties of quadratic equations
Vertex formula for parabolas

Suitable Grade Level

Grades 10-12