In Problems 9-12, find the indicated maximum or min- SECTION 4.2 Linear Programming: Graphical Methods 269 Imum value of the obiective function in the linear pro- gramming problem. Note that the feasible regions for these problems are found in the answers to Problems 19, 20, 23, and 24 in the Section 4.1 Exercises. 9. Maximize f= 30x + 50y subject to 21. Maximize f= x + 2y subject to x + y 2 4 2x + y s 8 ys 4 22. Maximize f= 3x + 5y subject to 2x + 4y 2 8 x+ 2y s 48 x + ys 30 2x + ys 50 3x + y s 7 ys 4 23. Minimizeg = 40x + 25y subject to x + y 2 100 x 2 0, y 10. Maximize f= 7x + 10y subject to -x + y s 20 3x + y s9 3x + 2y s 12 x + 2y s 8 x 2 0, y 2 0 11. Minimize g = 100x + 22y subject to - 2x + 3y N 30 24. Minimize g = 3x + 8y subject to 4x-5y 2 50 -x + 2y 2 4 x + y s 80 * + 3y 2 3 2x + 3y 2 5 2x + y 2 3 x 2 0, y 2 0 12. Minimize g = 12x + 8y subject to x + 2y 2 10 2x + y 2 11 x + y 2 9 x 2 0, y 2 0 APPLICATIONS 25. Manufacturing The Wellbuilt Company produces two types of wood chippers, economy and deluxe. The deluxe model requires 3 hours to assemble and 1/2 hour to paint, and the economy model requires 2 hours to assemble and 1 hour to paint. The maxi- mum number of assembly hours available is 24 per day, and the maximum number of painting hours available is 8 per day. If the profit on the deluxe model is $90 per unit and the profit on the economy model is $72 per unit, how many units of each model will maximize profit? (See Problem 27 in the Section 4.1 Exercises.) 26. Learning environments An experiment involving learning in animals requires placing white mice and rabbits into separate, controlled environments: environment I and environment II. The maximum amount of time available in environment I is 420 minutes, and the maximum amount of time available in environment II is 600 minutes. The white In Problems 13-24, solve the following linear program- ming problems. Restrict x 2 0 and y 2 0. 13. Maximizef = 3x + 4y subject to x + y s 6 2x + y s 10 ys 4 14. Maximizef = x + 3y subject to x + 4y s 12 ys 2 x + y s 9 15. Maximize f = 2x + 6y subject to x + ys 7 2x +ys 12 x + 3y s 15 16. Maximize f = 4x + 2y subject to x + 2y s 20 x + y s 12 4x + y s 36 17. Minimize g = 7x + 6y subject to 5x + 2y 2 16 3x + 7y 2 27 18. Minimize g = 22x + 17y subject to 8x + 5y 2 100 12x + 25y 2 360 19. Minimize g 3x + y subject to 4x + y 2 11 3x + 2y 2 12 noiesup boal o mice must spend 10 minutes in environment I and 25 minutes in environment II, and the rabbits must spend 15 minutes in environment I and 12 minutes in environment II, Find the maximum possible num- ber of animals that can be used in the experiment and find the number of white mice and the number of rabbits that can be used. (See Problem 28 in the Section 4.1 Exercises.) 27. Manufacturing A company manufactures two types of electric hedge trimmers, one of which is cordless. The cord-type trimmer requires 2 hours to make, and the cordless model requires 4 hours. The company has only 800 work hours to use in manufacturing each day, and the packaging department can package only 300 trimmers per day. If the company profits are $22.50 for the cord-type model and $45.00 for the cordless model, how many of each type should the company produce per day to maximize profits? 20. Minimizeg = 50x + 70y subject to 11x + 15y 2 225 x + 3y 2 27