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4 4 quadratic-curves

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4 4 quadratic-curves

1. 1. Quadratic Curves
2. 2. <ul><li>Supply, demand, cost, revenue, and profit functions can also be quadratic curves. </li></ul><ul><li>Examples: </li></ul><ul><li>Quadratic curves – plane curves with equations of the form </li></ul><ul><li>These curves are called conic sections . </li></ul>
3. 3. <ul><li>Types: Circle, Ellipse, Parabola, Hyperbola </li></ul><ul><li>For more information, read Section 3.2 of the book. </li></ul>
4. 4. <ul><li>1. Given the supply function S ( x ) = x 2 + 6 x + 9 and demand function D ( x ) = x 2 – 10 x + 25 , find the market equilibrium quantity and price. </li></ul>
5. 5. <ul><li>7. Given the demand function y D ( x + 4) = 400 and supply function 2 y S – x – 38 = 0 , find the market equilibrium quantity and price. </li></ul>
6. 6. <ul><li>9. Given the cost function C ( x ) = 1,250 + 20 x and revenue function R ( x ) = x (50 – 0.1 x ) , find the break-even quantity and price. </li></ul>
7. 7. <ul><li>19. When a particular computer accessory is sold for x pesos per unit, manufacturers will supply units to local retailers. The local demand would be 60 – x units. </li></ul><ul><li>At what market price will the manufacturers' supply of the items be equal to the consumers' demand for them? </li></ul><ul><li>How many units will be sold at this price? </li></ul>
8. 9. <ul><li>25. Assume that a company's cost and revenue functions are C ( x ) = 6 x + 120 and R ( x ) = 3 x 2 +48 x , respectively. </li></ul><ul><li>Find the break-even price and quantity. </li></ul><ul><li>Set up the profit function and use it to find the profit when 120 units are manufactured and sold. </li></ul>
9. 10. <ul><li>25. Assume that a company's cost and revenue functions are C ( x ) = 6 x + 120 and R ( x ) = 3 x 2 +48 x , respectively. </li></ul><ul><li>Find the break-even price and quantity. </li></ul>
10. 11. <ul><li>25. Assume that a company's cost and revenue functions are C ( x ) = 6 x + 120 and R ( x ) = 3 x 2 +48 x , respectively. </li></ul><ul><li>Set up the profit function and use it to find the profit when 120 units are manufactured and sold. </li></ul>
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