anonymous
  • anonymous
Factory motor assembles 2 types of motors, small and large. Cost of material is $15 for small motor and $30 for large. Two hours of labor are needed to assemble small motor and 6 hours for large motor. Cost of labor is $8/hr. Owner of the factory can allocate at most $1500/day for material and $1920/day for labor. Find the largest profit that owner can make if small motors are sold for $50 each and large motors for $100. Assume every motor produced is sold.
Mathematics
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SOLVED
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katieb
  • katieb
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dumbcow
  • dumbcow
Profit = revenue - cost revenue = price * quantity two types of revenue that from small motors and that from large motors x = number of small motors sold y = number of large motors sold total revenue = 50x + 100y There are two types of cost: labor and materials cost of labor is 8/hr one small motor takes 2hr or $16 large motor takes 6hr or $48 costLabor = 16x + 48y costMaterial = 15x+30y total cost = 31x + 78y Profit = revenue - cost profit = (50x+100y) -(31x+78y) profit = 19x + 22y Now we have to look at constraints: 1500/day for material so you cant spend more than 1500 on material 15x+30y < 1500 solve for y y < 50-1/2x 1920/day for labor 16x+48y <1920 solve for y y < 40 - 1/3x Graph these inequalities and they are bounded by x>0 and y>0 evaluate the vertices or end points around the edge of the shaded region bounded by the lines by putting the x,y values into profit equation you should get three points (0,40) -->you only sell large motors this yields profit of 880 (100,0) -->only sell small motors yields profit of 1900 where the lines meet 50-1/2x = 40-1/3x x = 60 y = 20 yielding profit of 1580 so largest profit is 1900 when only small motors are made and sold

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