Question

SOLVE IT BY HAND, NO EXCEL

Back Savers is a company that produces backpacks primarily for students. They are considering offering some combination of two different models—the Collegiate and the Mini. Both are made out of the same rip-resistant nylon fabric. Back Savers has a long-term contract with a supplier of the nylon and receives a 3600 square-foot shipment of the material each week. Each Collegiate requires 2.5 square feet while each Mini requires 1.5 square feet. The sales forecasts indicate that at most 900 Collegiates and 1100 Minis can be sold per week. Each Collegiate requires 45 minutes of labor to produce and generates a unit profit of $30. Each Mini requires 40 minutes of labor and generates a unit profit of $22. Back Savers has 35 laborers that each provides 40 hours of labor per week. Management wishes to know what quantity of each type of backpack to produce per week to maximize their profit.

Answer 1

Lot the company has to produce a numbers of collegiate and a numbers of Mini backpacks per wook to maximize the profile Since each collegiale generates $30 profit and each Mini generates $20 22 profit, so total profit is given by 2 =$(3 0x + 227) Since each collegiate requires 2.5 square feet and Mini requires 1.5 square feet of nylon tabric, so total nylon fibric required is (2.5x+1.50 square feet. . 2.58 +1-57 3 3650 Also, almost 900 colleginte and noo Minis can be sold per coook, therefore. x 900 y s 1100 Total labor required to produce a collegate and y Mini back pack is (45x + 404) minutes. Now available labor is 35x40 X Go - 84000 minutes. so, 45x+40y s 84500 Hence our problem is to Maximize, 2 = 30x+22y subject to 3.50 +1.54 s 3600 x sq0o y Slloo 45x+404 < 84 70o x y yo use graphical Method to solve the above problem. To draw the first constraints 2.5x+1.54 < 3600 treat it as 3-sx-tt-5 = 368 , when x=0 then = 24000 and when y=0, x= 1450 x o 1400 To draw the second constraint xc900 treat it as x goo. there line is partalled to Y axis. For third constraint y slloo treat it as y=1150 Here line is parallel to x-axis.

treat it as To draw the toweth constraint 45x+404 2 84000 45 x+4oy = 84000 xos AY 27. १८० Extrome point function Lines through Extreme point objective value 0 (0,0) 30.0 +22-0-0 5 6 X20 y yo A (900,0) 30x900+22X0 =27000 2 6 xx 900 y yo C (780, 1100) 1 -> 2-5+1.5733600 3 < 1100 30X780 +22x Ile 47 660 D (0, 1100) 3 y 21100 22x1100 - 24200 function is Hence maximum value of the objective 47 600 at x=780 and y= 1100 should produce 780 collegiate and a company Hoodini backpacks