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Write, graph and interpret the expense function. Write, graph and interpret the revenue function.Identify the points of intersection of the expense and revenue functions.
Identify breakeven points, and explain them in the context of the problem.
nonlinear function - revenue function - not a straight line.
second-degree equation - function has a variable raised to an exponent of 2
quadratic equation – 2nd degree equation
parabola - The graph of a quadratic equation
leading coefficient - a, in the quadratic equation
maximum value – parabola’s peak
vertex of a parabola – the point at the maximum value
axis of symmetry - vertical line that can be drawn through the vertex of the parabola so that the dissected parts of the parabola are mirror images of each other
A particular item in the Picasso Paints product line costs $7.00 each to manufacture. The fixed costs are $28,000. The demand function is q = –500p + 30,000 where q is the quantity the public will buy given the price, p. Graph the expense function in terms of price on the coordinate plane.
An electronics company manufactures earphones for portable music devices. Each earphone costs $5 to manufacture. Fixed costs are $20,000. The demand function is q = –200p + 40,000. Write the expense function in terms of q and determine a suitable viewing window for that function. Graph the expense function.
The revenue and expense functions are graphed on the same set of axes. The points of intersection are labeled A and B. Explain what is happening at those two points.