A manufacturing company makes two types of water skis, a trick ski and a slalom

Question

A manufacturing company makes two types of water skis, a trick ski and a slalom ski. The relevant manufacturing data are given in the table Labor-Hours per Ski Department Fabricating Finishing Maximum Labor-Hours Available per Day 384 36 Trick Ski 12 Slalom Ski f the profit on a trick ski is $50 and the profit on a slalom ski is $30, how many of each type of ski should be manufactured each day to realize a maximum profit? What is the maximum profit? The maximum profit is S The maximum occurs when trick skis and slalom skis are produced

Explanation / Answer

The maximum profit is 3400. The maximum occurs when 68 trick skis and 0 slalom skis are produced  

Fabricating Finishing Trick ski Slalom ski Trick ski Profit Slalom ski Profit Total profit Trick ski Slalom ski Trick ski Profit Slalom ski Profit Total profit 0 48 0 1440 1440 0 36 0 1080 1080 1 46.5 50 1395 1445 1 35 50 1050 1100 2 45 100 1350 1450 2 34 100 1020 1120 3 43.5 150 1305 1455 3 33 150 990 1140 4 42 200 1260 1460 4 32 200 960 1160 5 40.5 250 1215 1465 5 31 250 930 1180 6 39 300 1170 1470 6 30 300 900 1200 7 37.5 350 1125 1475 7 29 350 870 1220 8 36 400 1080 1480 8 28 400 840 1240 9 34.5 450 1035 1485 9 27 450 810 1260 10 33 500 990 1490 10 26 500 780 1280 11 31.5 550 945 1495 11 25 550 750 1300 12 30 600 900 1500 12 24 600 720 1320 13 28.5 650 855 1505 13 23 650 690 1340 14 27 700 810 1510 14 22 700 660 1360 15 25.5 750 765 1515 15 21 750 630 1380 16 24 800 720 1520 16 20 800 600 1400 17 22.5 850 675 1525 17 19 850 570 1420 18 21 900 630 1530 18 18 900 540 1440 19 19.5 950 585 1535 19 17 950 510 1460 20 18 1000 540 1540 20 16 1000 480 1480 21 16.5 1050 495 1545 21 15 1050 450 1500 22 15 1100 450 1550 22 14 1100 420 1520 23 13.5 1150 405 1555 23 13 1150 390 1540 24 12 1200 360 1560 24 12 1200 360 1560 25 10.5 1250 315 1565 25 11 1250 330 1580 26 9 1300 270 1570 26 10 1300 300 1600 27 7.5 1350 225 1575 27 9 1350 270 1620 28 6 1400 180 1580 28 8 1400 240 1640 29 4.5 1450 135 1585 29 7 1450 210 1660 30 3 1500 90 1590 30 6 1500 180 1680 31 1.5 1550 45 1595 31 5 1550 150 1700 32 0 1600 0 1600 32 4 1600 120 1720 33 3 1650 90 1740 34 2 1700 60 1760 35 1 1750 30 1780 36 0 1800 0 1800

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