AlgH Chapter 4 Review Sheet Date Wk # ) x z x y 8 y 9z 4 ) y 0 7y ) 6 7 8 x y 5 4 x y x y z 7 4) x y z 0 f ( x) x 5 Let g( x) 7 h( x) 4 x 5) f (h()) 6) h (g()) 7) f ( f ( )) 8) g ( f ( 5)) h 0) h ( ) ) f ( g( x)) ) g( 4 a) 9) ( g( x))
) Hamburger Problem Wk # Sue Flay and Cassa Roll obtain a franchise to operate a hamburger stand for a well known national hamburger chain. They pay $0,000 for the franchise, and have additional expenses of $50 per thousand hamburgers they sell. They sell the hamburgers for $.75 each, so they take in revenue of $750 per thousand burgers. (a) Let r(x) be the number of dollars revenue they take in by selling x thousand burgers. Write the particular equation. (b) Find r(0), r(50), and r(0) (c) Let c(x) be the total cost of owning the hamburger stand, including the $0,000 franchise fee. Write the particular equation for function c. (d) Find c(0), c(50), and c(0) (e) Sketch the graphs of r and c on the same set of axes. Have they crossed by the time x is 50? (f) How many burgers must Sue and Cassa sell in order to break even? 4) 6z x y 4z 5 7y 5 5) 6x y z 7 5 x y z 4 6) Write a set of inequalities that describes the shaded region. (Note: The lines are labeled,,, 4) (-6,) (0,0) 4 (5, 0) (-6,4) (,0)
Wk # 7. CB Radio Manufacturing Problem Suppose you work for a small company that makes high-quality CB radios. They wish to optimize the numbers of the two models they produce, Good Buddies and Breakers, in order to maximize their profit. Since you are an expert at linear programming, your boss assigns you the job. You find the following information: i. The assembly lines can produce no more than 6 Good Buddies and 5 Breakers per day. ii. No more than radios, total, can be produced per day. iii. They can spend a total of no more than 89 man-hours a day assembling radios. It takes man-hours to assemble a Good Buddy and 7 man-hours to assemble a Breaker. iv. They can spend at most 68 man-hours per day, total, testing radios. It takes 4 man-hours to test a Good Buddy and man-hour to test a Breaker. v. The number of Breakers produced per day must be more than half the number of Good Buddies. Using this information, answer the following questions: a. Define the variables. (Let the independent variable be the Good Buddies so everyone has the same graph) b. If the company makes a profit of $0 on each Good Buddy and $40 on each Breaker, write an equation expressing dollars profit earned per day in terms of the numbers of Good Buddies and Breakers produced each day. (Objective Function) c. Write the set of inequalities (Constraints) for each of the requirements i-v above. 8. Continue problem 7: d. On graph paper, plot the graph of the feasible region. Use highlighter to shade the feasible region. e. Label the corner points of the feasible region with letters. Determine all the exact coordinates of each point. f. Shade the portion of the feasible region in which the daily profit is at least $960. g. Find the optimum point at which the daily profit is a maximum, and the number of dollars they would earn per day by operating at this point.
Solutions to Chapter 4 Review Sheet Wk# Solutions to Wk # 8 45. (,,5)., 4 4 7., 5 4. Dependent---consistent (all pts on line) 5. 7 6. 4 7. 8. 5 9. 9 5x 66 x 0. 4. 6x 9. a 5. 4.,, 5 5. No solution --- inconsistent (independent) Be sure to show algebraically!!! 6. ) y x 0 ) y x ) x 6 0 4) y x 40 4
Solution #7-8 solutions to Wk # a. Let x = # Good Buddies produced per day Let y = # Breakers produced per day Let P = # dollars profit per day b. MAX: P = 0x + 40y c. Subject to: ) x > 0 ) y > 0 ) x < 6 or 0 < x < 6 4) y < 5 0 < y < 5 5) x + y < 6) + 7y < 89 7) 4x + y < 68 8) y > ½ x 5