University:
Winston-Salem Forsyth County Schools
Course:
AP Calculus AB
Academic year:

2014
Views:

75

Pages:

2
Author:

ingridurman76k

Algebra II WS U6 L4 Linear Programming Word Problems Name ) A sporting goods manufacturer produces skateboards and in-line skates. Its dealers demand at least 30 skateboards per day and 20 pairs of in-line skates per day. The factory can make at most 60 skateboards and 40 pairs of in-line skates per day. The total number of skateboards and pairs of in-line skates cannot exceed 90. The profit on each skateboard is $12 and the profit on each pair of in-line skates is $18. How many of each product should the company manufacture to get the maximum profit? xeskateboard y= skates • X ≥ 30 (30,20) = 720 • y = 20 г (30,40) = 1080 • X ≤ 60 (50,40) = 1320 • y≤ 40 (60,20) = 1080 • xty ≤ 90 (160, 30) = 1260 9 ≤ -x+90 40 3° 20 f(x,y) = 12x +/By → X 10 20 30 40 50 skateboards 40 skates 2) A bakery is making whole-wheat bread and apple bran muffins. For each batch of bread they make $35 profit. For each batch of muffins they make $10 profit. The bread takes 4 hours to prepare and 1 hour to bake. The muffins take .5 hours to prepare and .5 hours to bake. The maximum preparation time available is 16 hours and the maximum bake time is 10 hours. How many batches of bread and muffins should be made to maximize profits? Xibread y:muffin • Prep bake 4x7.5y ≤ 16 x +. 5y ≤ 10 {y ≤-x+10 y 5-2x+20 f(x,y) = 35x+10y (0,0) = 0 (0,20) = 200 (2, 16) = 230 (4,0) = 140 4х716 y≤ - 8x +32 2 bread 16 muffin 3) The area of a parking lot is 600 square meters. A car requires 6 square meters and a bus requires 30| square meters of space. The lot can handle a maximum of 60 vehicles. If a car costs $3 and a bus cost $8 to park in the lot, determine the number of each vehicle to maximize the amount collected. x: car y: bus • 6x + 30y ≤ 600 : 30y 5 - lo x 16000 • x+y = 60 (0,0) =0 (0,20) = 160 (50,10) = 230 (60, 0) =180 f(x. y) = 3x + By лати 50 cars 1o buses 5 10 15 20 25 omit The manufacturing facility that supplies a chain of Packaging Plus stores received a rush order for 290 boxes. It had to fill the order in eight hours or less. The factory has a machine that can produce 30 boxes per hour and cost $15 per hour to operate. The factory can also use two student workers from other, less- urgent tasks; together those students can make 25 boxes per hour at a cost of $10 per hour. What combination of machine and student work times will meet the order deadline for least total cost? X: machine y: students 00% 30X + 25y ≤290 25y≤-30x1290 • x+ y ≤ 8 y≤-xj8 (11.6) f(x,y) = 15x+ 10 y