1 Productivity A time study showed that on average the productivity of a worker after t 2 3 hours on the job can be modeled by P 29t 9t t 0 t 8 where P is the number of units produced per hour After how many hours will productivity be maximized A 3 33 hours B 8 00 hours C 6 58 hours D 2 96 hours E 2 32 hours 2 Productivity A time study showed that on average the productivity of a worker after t 2 3 hours on the job can be modeled by P 14t 7t t 0 t 8 where P is the number of units produced per hour What is the maximum productivity Round your answer to the nearest whole number of units A 132 units B 80 units C 103 units D 281 units E 171 units 3 Productivity A time study showed that on average the productivity of a worker after t 2 3 hours on the job can be modeled by P 18t 7t t 0 t 8 where P is the number of units produced per hour What is the maximum productivity Round your answer to the nearest whole number of units A 198 units B 152 units C 179 units D 122 units E 286 units 4 Return to sales The manufacturer of GRIPPER tires modeled its return to sales with television advertising expenditures in two regions as follows Region 1 S1 20 40 x1 0 3 x12 Region 2 S2 10 30 x2 1 2 x22 S where S1 and 2 are the sales revenue in millions of dollars and x1 and x2 are millions of dollars of expenditures for television advertising How much money will be needed to maximize sales revenue in both districts A 5 million B 106 million C 100 million D 22 million E 52 million 5 Candidate recognition Suppose that in an election year the proportion p of voters who recognize a certain candidate s name t months after the campaign started is given by 5 3t p t 2 0 3 t 49 After how many months is the proportion maximized A 3 months B 8 months C 4 months D 7 months E 2 months 6 Minimum fence The running yard for a dog kennel must contain at least 625 square feet If a 20 foot side of the kennel is used as part of one side of a rectangular yard with 625 square feet what dimensions will require the least amount of fencing A D 62 5 ft by 10 ft 30 ft by 7 5 ft B E 625 ft by 1 ft 125 ft by 5 ft C 25 ft by 25 ft 7 Minimum cost From a tract of land a developer plans to fence a rectangular region and then divide it into two identical rectangular lots by putting a fence down the middle Suppose that the fence for the outside boundary costs 6 per foot and the fence for the middle costs 3 per foot If each lot contains 2500 square feet find the dimensions of each lot that yield the minimum cost for the fence A Dimensions are 61 93 ft for the side parallel to the divider and 67 82 ft for the other side B Dimensions are 67 82 ft for the side parallel to the divider and 61 93 ft for the other side C Dimensions are 64 81 ft for the side parallel to the divider and 64 81 ft for the other side D Dimensions are 60 00 ft for the side parallel to the divider and 70 00 ft for the other side E Dimensions are 70 00 ft for the side parallel to the divider and 60 00 ft for the other side 8 Optimization at a fixed cost A rectangular area is to be enclosed and divided into thirds The family has 900 to spend for the fencing material The outside fence costs 14 per running foot installed and the dividers cost 24 per running foot installed What are the dimensions that will maximize the area enclosed A Dimensions are 4 90 ft for the side parallel to the dividers and 11 70 ft for the other side B Dimensions are 11 70 ft for the side parallel to the dividers and 4 90 ft for the other side C Dimensions are 4 90 ft for the side parallel to the dividers and 11 70 ft for the other side D Dimensions are 6 67 ft for the side parallel to the dividers and 19 99 ft for the other side E Dimensions are 19 99 ft for the side parallel to the dividers and 6 67 ft for the other side 9 Volume A rectangular box with a square base is to be formed from a square piece of metal with 42 inch sides If a square piece with side x is cut from each corner of the metal and the sides are folded up to form an open box the volume of the box is V 18 2 x 2 x What value of x will maximize the volume of the box A 21 B 17 C 7 D 13 E 20 10 Revenue The owner of an orange grove must decide when to pick one variety of oranges She can sell them for 6 a bushel if she sells them now with each tree yielding an average of 3 bushels The yield increases by half a bushel per week for the next 10 weeks but the price per bushel decreases by 0 30 per bushel each week When should the oranges be picked for maximum return A 2 weeks from now D 4 weeks from now B 8 weeks from now E 3 weeks from now C 7 weeks from now