A furniture manufacturer produces chairs and sofas. The chairs require 20 feet of wood, 1 lb. of foam rubber, and 2 square yards of material. The sofas require 100 feet of wood, 50 Ibs. of foam rubber, and 20 square yards of material. The manufacturer has in stock 1900 feet of wood, 500 Ibs. of foam rubber, and 240 square yards of material. If the chairs can be sold for $20 each and the sofas for $300 each, how many of each should be produced to maximize the income?

Answer:In order to maximize profit of $3700 we need to produce 50 units of Chairs and 9 units of SofaStep-by-step explanation: Let X be the number of units of Chairs produced and Y be the number of units of Sofa to be produced                           wood    foam rubber  square yards of material  Selling PriceChairs                  20X           1X                 2X                       =            $20XSofa                      100Y       50Y               20Y                      =           $300Y                              1900        500               24020x+100y=1900x+50y=5002x+20y=240use equation 2 to find the value of xx= 500-50ySubstitute value of x in equation 32(500-50y) + 20y= 2401000-100y + 20y = 2401000-240 = 100y-20y 760 = 80yy= 9.5 ≈ 9 units ( since we can't make half of any product )Put value of y in equation 2x= 500- 50 ( 9)x= 50 unitsMaximize profit = 20X + 300Y                           = 20(50) + 300( 9)                           = $3700