1. [-/2 Points] DETAILS HARMATHAP12 2.2.031. MY NOTES ASK YOUR TEACHER The monthly profit from the sale of a product is given by P = 16x - 0.1x2 - 100 dollars. (a) What level of production maximizes profit? units (b) What is the maximum possible profit? Need Help? Read it Watch It Submit Answer 2. [-/4 Points] DETAILS HARMATHAP12 2.2.003. MY NOTES ASK YOUR TEACHER Consider the following equation. y = 5 + 8x - x2 (a) Find the vertex of the graph of the equation. (x, y) = (b) Determine whether the vertex is a maximum or minimum point. O maximum O minimum (c) Determine what value of x gives the optimal value of the function. X = (d) Determine the optimal (maximum or minimum) value of the function. V = Need Help? Read It Submit Answer3. [-/4 Points] DETAILS HARMATHAP12 2.2.005. MY NOTES ASK YOUR TEACHER Consider the following equation. f( x) = 2x - x2 (a) Find the vertex of the graph of the equation. ( x, y ) = ( (b) Determine whether the vertex is a maximum or minimum point. O maximum minimum (c) Determine what value of x gives the optimal value of the function. (d) Determine the optimal (maximum or minimum) value of the function. f ( x ) = Need Help? Read It Submit Answer4. [-/3 Points] DETAILS HARMATHAP12 2.2.048. MY NOTES ASK YOUR TEACHER Suppose the percent of the total work force that is female is given by p(t) = -0.0036t2 + 0.48t + 33 where t is the number of years past 1970. (a) Graph the function y = p(t). y 70 70 60 60 60 50 50 50 50 40 40 40 10 30 30 30 30 20 20 20 20 10 10 10 10 -+ t O 50 100 150 200 AO 50 100 150 200 50 100 150 200 AO 50 100 150 200 A (b) From the equation, identify the maximum point on the graph of y = p(t). (Round your answers to two decimal places.) (t, y) = ( (c) In what year is the percent of women workers at its maximum, according to this model? Need Help? Read It Submit Answer5. [-/1 Points] DETAILS HARMATHAP12 2.3.007. MY NOTES ASK YOUR TEACHER Find the maximum revenue for the revenue function R(x) = 362x - 0.6x2. (Round your answer to the nearest cent.) R = $ Need Help? Read It Submit Answer 6. [-/2 Points] DETAILS HARMATHAP12 2.3.011. MY NOTES ASK YOUR TEACHER The profit function for a certain commodity is P(x) = 120x - x2 - 1000. Find the level of production that yields maximum profit, and find the maximum profit. X = units P = $ Need Help? Read it Watch It Submit Answer 7. [-/1 Points] DETAILS HARMATHAP12 2.3.010. MY NOTES ASK YOUR TEACHER If, in a monopoly market, the demand for a product is p = 4400 - x and the revenue is R = px, where x is the number of units sold, what price will maximize revenue? Need Help? Read It Watch It Submit Answer 8. [-/2 Points] DETAILS HARMATHAP12 2.3.025. MY NOTES ASK YOUR TEACHER If the supply function for a commodity is p = q2 + 2q + 16 and the demand function is p = -8q2 + 5q + 436, find the equilibrium quantity and equilibrium price. equilibrium quantity equilibrium price Need Help? Read It Watch It Submit Answer 9. [-/2 Points] DETAILS HARMATHAP12 2.3.029. MY NOTES ASK YOUR TEACHER If the supply and demand functions for a commodity are given by p - q = 10 and q(2p - 10) = 300, what is the equilibrium price and what is the corresponding number of units supplied and demanded? equilibrium price number of units units Need Help? Read it Watch It Submit