Date:______Block:______Name:______
Linear Programming
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1. A manufacturer of motorized scooters produces two types: budget and deluxe. The budget scooter requires 5 hours of assembly time and 2 hours of testing time. The deluxe model requires 10 hours of assembly time and 1 hour of testing time. In a week, there are 110 hours for assembly and 26 hours for testing. The profits for the budget and deluxe models are $78 and $149 respectively. How many of each type should be produced per week to maximize profit?
2. A new manufacturer of inflatable rafts is planning to produce two models of rafts: child rafts and large rafts. The child raft requires 5 hours of assembly. The large raft requires 6 hours of assembly time. In addition, the child raft uses 10m2 of fabric, while the large raft uses 19m2. In a week, there are 150 hours for assembly and 190m2 of fabric available. The profits for the child and large rafts are $120 and $350 respectively. How many of each type of raft should this manufacturer produce to maximize profit?
3. A factory manufactures roller blades and hockey skates. A pair of roller blades requires 28 minutes of machine time and 35 minutes of labour. A pair of hockey skates requires 70 minutes of machine time and 25 minutes of labour. The factory restricts the machine to 700 min per day and allows for 875 min of labour per day. The profits on roller blades and skates are $41.50 and $38.00 per pair respectively. Determine how many pairs of each need to be made per day to maximize profit.
4. It takes a tailoring company 2 hours of cutting and 4 hours of sewing to make a wool jacket. To make a cotton jacket, it takes 4 hours of cutting and 2 hours of sewing. At most, 20 hours per day are available for cutting and 16 hours are available for sewing. If the profit on a wool jacket is $34 and on a cotton jacket they make $31, how many of each type should they produce a day to maximize the profit?
5. A company manufactures bicycles and tricycles. It takes 2 hours to assemble a bicycle. It takes 1 hour to assemble a tricycle. The assembly machine is available for only 100 hours each month. The maximum number of bicycles and tricycles that can be made each month is 80. The profit on a bicycle is $50, and the profit on a tricycle is $30. How many bicycles and tricycles should be manufactured in a month to produce the maximum profit?
6. To manufacture cushions and pillows, a firm uses two machines (A and B). Pillows require 2 minutes on Machine A and 5 minutes on Machine B. Cushions require 9 minutes on Machine A and 9 minutes on machine B. Machine A is available for 6 hours a day. Machine B is available for 10 hours and 30 minutes per day. If the profit made on a cushion is $3.20, and the profit on a pillow is $1.20, find out how many pillows and cushions should be made to obtain a maximum profit.
7. Karen and Paul, two employees of a hockey-stick manufacturer, both make hockey sticks and goalie sticks. Karen can make 3 hockey sticks and 3 goalie sticks per hour. Paul can make 1 hockey stick and 4 goalie sticks per hour. At least 12 hockey sticks and 30 goalie sticks need to be made each day. If Karen earns $7 per hour and Paul earns $6 per hour, then how long should each person spend making the hockey sticks and goalie sticks to minimize the cost?