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
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