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Topic 3 - UKEQ1013 Quantitative Techniques I(May 2015...

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UKEQ1013 Quantitative Techniques I (May 2015) 52 UNIVERSITI TUNKU ABDUL RAHMAN FACULTY OF ACCOUNTANCY AND MANAGEMENT ACADEMIC YEAR 2015/2016 TUTORIAL 7 (Questions) Self-Practice Questions 1. Find the graphical solution of the inequality: (a) 3 x 6 > 0. (b) 2 y + 8 ≤ 0. (c) 2 x + 3 y < 6. (d) 3 x 4 y 12. (e) 2 x + y 2. (f) x 10 y > 0. 2. Write the system of inequalities that describes the shaded region. (a) (b) (c) (d) 3. Determine the solution set for this system of inequalities graphically: (a) 3 x + y > 3, 2 x y 4 (b) x y 1, 4 x + 3 y 12, x 0, y 0 (c) 2 x + y 6, x + 3 y 6, x 0, y 0 (d) y x + 1, y x 1, y 0, x 0 (e) y x 1, 2 y x + 2, y + x 3, y 0, x 0
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UKEQ1013 Quantitative Techniques I (May 2015) 53 4. Formulate, but do not solve, a linear program for the following scenario. A boat manufacturer makes fishing boats, which are sold for a profit of RM 500 each, and canoes, which are sold for a profit of RM 400 each. Each fishing boat requires 100 assembly hours and 25 finishing hours, while each canoe requires 75 assembly hours and 50 finishing hours. The manufacturer has a total of 8000 assembly hours and 3000 finishing hours available. How many fishing boats and how many canoes should be made to maximize the manufacturer‟s profit? (Let x = the number of fishing boats and y = the number of canoes.) ( Answer: Maximize P = 500x + 400y subject to 100x + 75y ≤ 8000 25x + 50y ≤ 3000 x 0, y 0 ) 5. Formulate, but do not solve, a linear program for the following scenario. A supplier has on hand 200, 300 and 120 units of raw materials A, B and C, respectively. The company produces two products requiring the number of units of each raw material listed in the table below. Product I sells for RM 200 and product II for RM 350. If the company wishes to maximize the gross income, how many of each product should be produced? (Let x = the number of items of Product I and y = the number of items of Product II.) Product I Product II Raw Material A (units) 3 2 Raw Material B (units) 4 5 Raw Material C (units) 2 1 ( Answer: Maximize I = 200x + 350y subject to 3x + 2y ≤ 200 4x + 5y ≤ 300 2x + y ≤ 120 x 0, y 0 ) 6. (a) A fruit seller sells only cikus and starfruits. All the fruits are sold in packets. Cikus are sold in packets that consist of 6 cikus per packet with the price of RM5. Starfruits are sold in packets that consist of 4 starfruits per packet with the price of RM6. If he sells x packets of cikus and y packets of starfruits a day, write an inequality in terms of x and y that satisfies each of the following constraints: (i). He sells at least 15 packets of cikus. (ii). He sells at least 20 packets of starfruits. (iii). He sells at least 40 packets of fruits altogether. (iv). The total number of fruits sold by him is not more than 340. (v). The value of sales of fruits is not less than RM150. (b) A factory has x skilled workers and y less-skilled workers. Write an inequality in terms of x and y that satisfies each of the following constraints.
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