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Linear Programming WS #1 This is to help you get started on this worksheet since I am out with my son. So take advantage of this help instead of just copying it down! THINK about what is being done in the problem. #1 The area of a parking lot is 600 square meters. A car requires 6 square meters. A bus requires 30 square meters. The attendant can handle only 60 vehicles. If a car is charged $2.50 and a bus $7.50, how many of each should be accepted to maximize income? a) Identify whether you will maximize or minimize. MAXIMIZE b) define your variables. Let c = Cars and b = Bus c) write an objective function to be maximized or minimized. P(c, b) = 2.50c + 7.50b d) write a system of inequalities for the constraints. e) graph the system of inequalities. f) find the coordinates of the vertices of the feasible region in the objective function. (0, 20) (50, 10) (60, 0) g) substitute the coordinates of the vertices of the feasible region in the objective function P(c, b) = 2.50c + 7.50b. h) the greatest or least result to answer the question. To maximize income there will need to be 50 cars and 10 buses in the parking lot. AGAIN!!!This is to help you get started on this worksheet since I am out with my son. So take advantage of this help instead of just copying it down! THINK about what is being done in the problem. #2 The B & W Leather Company wants to add handmade belts and wallets to its product line. Each belt nets the company $18 in profit, and each wallet nets $12. Both belts and wallets require cutting and sewing. Belts require 2 hours of cutting time and 6 hours of sewing time. Wallets require 3 hours of cutting time and 3 hours of sewing time. If the cutting machine is available 12 hours a week and the sewing machine is available 18 hours per week, what ratio of belts and wallets will produce the most profit within the constraints? a) b) c) d) Identify whether you will maximize or minimize. MAXIMIZE define your variables. Let b = belts and w = wallets write an objective function to be maximized or minimized. P(b, w) = 18b + 12w write a system of inequalities for the constraints. e) graph the system of inequalities. f) find the coordinates of the vertices of the feasible region in the objective function. (0, 4) (1.5, 3) (3, 0) g) substitute the coordinates of the vertices of the feasible region in the objective function P(b, w) = 18b + 12w. h) the greatest or least result to answer the question. There will need to be 1.5 belts and 3 wallets to maximize profit. Assignment • Finish the rest of Worksheet #2 in class and what you do not finish is homework. • WE WILL BE GRADING THIS IN CLASS FIRST THING TOMORROW!!!!!