MATH 1324 | Lab 3 Chapter 3, Appendix A

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Math 1324 Name Lab 3 3.1-3.6, Appendix A Instructions: Work each of the following problems in the space provided. You must show all work to receive full credit. Simplify and clearly indicate all answers. 1. Suppose a company has a cost function of C(x)= %xz +222x+ 2800 where x is the total number of units produced. The selling price is given by the equation [1250 %YJ dollars per unit. a. Write an equation for the revenue function R(x). Hint: R(x)=x- p(x) or Revenue = (Number of items) (Price per item) b. Find the equation of the profit function P(x). Show work. Hint: P(x)=R(x)C(x) or Profit=Revenue - Cost . Using the profit function P(x), find the maximum profit and the number of units that must be sold to maximize profit. Show work to receive credit. Hint: Find the vertex. Write the answer in a complete sentence. Sentence(s): 2. If the supply function for a commodity is p = + 8 +16 and the demand functionis p =3 +6+36, find the equilibrium quantity and equilibrium price. Show algebraic work. With a complete sentence explain the meaning of your answers. Equilibrium Quantity: Equilibrium Price: Sentence(s): 3. A company has total costs C(x) = 15000+ 35x + 0.1x? and total revenue given by R(x) = 385x 0.9x*. Find the break-even point(s). Show work. HINT: Remember the break-even point is the point with the coordinates (x, C(x)), when Cost = Revenue. It could be more than one point. Remember to state both coordinates of the break-even point (or points)! Break-Even Point #1: Break-Even Point #2: -2 4. Use the given graph to answer the following questions. (Worth 10 points) a. State the coordinates of the x-intercept(s). b. State the coordinates of the y-intercept. | | 7 c. State the domain in mterval notation. Use interval notation. 1234567( d. State the range in interval notation. Use interval notation. 5. For the functions f{x) = 5x*> 2x + 9 and g(x) = 8x 4 a. Find and simplify (/- g)(x) b. Find and simplify (g f)(x) c. Find the difference quotient, W' for f. 6. Let k(x) =x* 9x? a. State the degree of the given polynomial. b. What 1s the most total number of peaks and valleys of the graph of the given polynomial? Hint: How many turns? c. Find the x-intercepts of k&(x). Show work for credit. x-intercept point #1: x-intercept point #2: x-intercept point #3: d. Graph the general shape of the given polynomial. Label units on x-axis. 7. A taxi driver must pay a daily fee of $80 to the cab company and has marginal costs of $0.90 per mile. a. Find the daily cost function C(x) and define what x represents. b. Find the average cost function C (x). . Find C(70). (Write the equation used for full credit.) d. Find (350). (Write the equation used for full credit.) e. Find the horizontal asymptote of C(x), and explain what it means in practical terms. Use complete sentence(s)