1. If the profit from the sale of x units of a product is P = 105x − 300 − x2, what level(s) of production will yield a profit of $1050? (Enter your answers as a comma-separated list.) x = _________ units 2. The total costs for a company are given by C(x) = 5400 + 80x + x2 and the total revenues are given by R(x) = 230x. Find the break-even points. (Enter your answers as a comma-separated list.) x= __________ units 3. If total costs are C(x) = 900 + 800x and total revenues are R(x) = 900x − x2, find the break-even points. (Enter your answers as a comma-separated list.) x= _____________ 4. For the years since 2001, the percent p of high school seniors who have tried marijuana can be considered as a function of time t according to p = f(t) = 0.17t2 − 2.61t + 52.64 where t is the number of years past 2000.† In what year after 2000 is the percent predicted to reach 75%, if this function remains valid? _______________ 5. Using data from 2002 and with projections to 2024, total annual expenditures for national health care (in billions of dollars) can be described by E = 4.61x2 + 43.4x + 1620 where x is the number of years past 2000.† If the pattern indicated by the model remains valid, in what year does the model predict these expenditures will reach $15,315 billion? __________________ 6. The monthly profit from the sale of a product is given by P = 32x − 0.2x2 − 150 dollars. (a) What level of production maximizes profit? ___________ units (b) What is the maximum possible profit? $_____________ 7. Consider the following equation. y = 9 + 6x − x2 (a) Find the vertex of the graph of the equation. (x, y) = (__________) (b) Determine what value of x gives the optimal value of the function. x=_____________ (c) Determine the optimal (maximum or minimum) value of the function. y=______________ 8. Consider the following equation. f(x) = 6x − x2 (a) Find the vertex of the graph of the equation. (x, y) = (__________) (b) Determine what value of x gives the optimal value of the function. x=_____________ (c) Determine the optimal (maximum or minimum) value of the function. f(x)= _____________ 9. Find the maximum revenue for the revenue function R(x) = 358x − 0.7x2. (Round your answer to the nearest cent.) R = $______________ 10. The profit function for a certain commodity is P(x) = 150x − x2 − 1000. Find the level of production that yields maximum profit, and find the maximum profit. x= _________ units P=$ _________ 11. If, in a monopoly market, the demand for a product is p = 2000 − x and the revenue is R = px, where x is the number of units sold, what price will maximize revenue? $________________ 12. If the supply function for a commodity is p = q2 + 6q + 16 and the demand function is p = −3q2 + 4q + 436, find the equilibrium quantity and equilibrium price. equilibrium quantity_______________ equilibrium price $_______________ 13. If the supply and demand functions for a commodity are given by p ...