4 6 - | temp-bs11-2- - - Mann Enterprises is a Houston manufacturer of tables and accessories for personal computers. The company is caught in a vicious crossfire between rapidly dropping market prices from competitors worldwide for its products and stable domestic costs for its materials. The 15 different products noted below must be scheduled to maximize profits or there will be no jobs and no fim in another 3 months. Your job as the new OM graduate is to address the issues raised this morning by Laura Mann, the president in an emergency meeting in her office Without being told so explicitly, you conclude that if you don't get the schedule done accurately and in a timely manner, you will be history to your relief, the industrial engineers and accountants have provided the data shown below. The issues, as recorded in your notes, are Indented in (a) through Minimum Steel Alloy Plastic Wood Aluminum Formica Labor Monthly Required Required Required Required Required Required Demand Contribution Product (Lb.) (Sq. FL) (Bd. FL.) Lb.) (Bd. FL.) (Hr.) (Units) to Profit A158 0.4 0.7 5.8 10.9 3.1 $18.79 B179 05 18 10.3 2.0 10 20 6.31 C023 1.5 1.1 23 1.2 10 8.19 0045 10 0.4 20 4.8 10 45.88 E388 12 12 1.2 8.1 4.9 5.5 63.00 F422 1.4 1.5 7.1 10.0 0.8 20 4.10 G366 10 14 70 6.2 11.1 9.1 10 81.15 H600 5 1.0 5.0 7.3 1224 4.8 20 50.08 1701 0.4 10.0 52 1.9 50 12.79 J802 1 0.3 11.0 6.1 1.4 20 15.88 K900 0.2 12.5 7.7 1.0 20 17.91 L901 2 1.8 1.5 13.1 5.0 5.1 10 49.99 MOSO 27 5.0 2.1 3.1 20 24.00 N150 10 1.1 5.8 77 10 88.88 P259 10 6.2 150 1.0 6.6 10 77.01 Availability 980 400 600 per month 2.500 1.800 1.000 Specify the objective function and constraints for the problem. . Let X monthly production quantity of a product beginning with letter i Objective function round your responses to two decimal places Maximize = 18.79XA 6.31%, * 8.1945.88X, 63.00X + 4.10X81.15X50.05X 12.79%, * 15,88%, + 17.91 X 49.99 X 26 X 68.88 x 77.01 X Constraints jenter your responses as whole numbera): Material constraints. Steel Alloy (C) 4X6X10X12X10X, 5X +X+X, 2X + 10X, 10X5980 Plastic (2) 4X4,5X, 4X 1.2X 1.4X 1.4X1.0X, + 4X, 3X, 2x 1.8X2.7% 1.1X, S 400 7X * 1.8X, 1.5% 2.0% 12X1.5X + 7.0% Wood (C). 5.0%, * 1.5X 5.0% + 5.8%, + 6.2% 3 600 Aluminium (C) 5.8XX+10.3Xg. 1.1X + 8.1X.7.1%6.2% + 7.3X10.0x + 11.0%,. 12.5%+ 13.1X, 15.0X, $ 2500 Formica (C) 10,9%A20X32.3X + 4.9X 10.0% 11.1X, +124X5.2X + 6.1X, +7.7% + 5.0% 21% 1.0% 5 1800 Labor constraint (c) 3.1X, 10X12X4.BX 5.5X, 8X, 9.1%. 4.8% +1.9%,+ 1.4X, 10X +5.1X3.1X, +7TXN 6.6X, S 1000 Minimum demand constraints: C, XA20 ( CX, 20 (C) Xc10 co Xp 210 (C): X,20 C X 220 Cal X.210 Cik X220 C.sk X250 O X220 (C: X20 ( X 210 (Cut x 2 C X 220 (C): X2 : X 10 (Cy Xp 2 Alinear programming software shows the following solution Click the icon to view the data concerning products Click the icon to view the data concerning constraints. . a) Only product A158 is not produced, by bi Clearly explain the meaning of each shadow orice Product Optimal Value Original Coefficient Lower Limit Upper Limit XA 0 20 Reduced Cost 1.32373 0 0 18.79 6.31 20.11373 52.49662 10 8.19 45.88 10 0 0 0 XB Xc Xo XE F XG XH XI Xj XK XL XN 11.507 20 10 20 0 0 - Infinity - Infinity - Infinity - Infinity 59.01673 - Infinity - Infinity - Infinity - Infinity - Infinity - Infinity 47.34072 - Infinity 80.82936 - Infinity 34.64475 48.41532 77.38298 31.47013 115.1911 82.73582 24.539 26.7216 27.28386 56.43208 53.243 50 0 63 4.1 81.15 50.06 12.79 15.88 17.91 49.99 24 88.88 77.01 20 20 0 0 0 0 54.945 20 12.202 10 0 0 126.4764 125.8801 Xp Data Table Constraint Lower Limit Upper Limit Original RHS 980 C1 C2 C3 Shadow Prices 2.711812 0 10.6486 2.182708 0 0 Slack or Surplus 0 113.866 0 0 258.885 8.52954 400 600 2500 1800 CA C5 co 0 C7 C8 0 1000 0 20 10 10 0 0 11.5072 0 20 Cg C10 C11 C12 C13 C14 C15 C16 C17 C18 861.5504 286.1337 587.7851 1889.72 1541.115 991.4705 - Infinity 17.91737 5.041353 0 - Infinity 16.50255 3.532913 17.09391 39.20661 14.30611 15.88757 - Infinity 15.45261 - Infinity 8.355577 0 -46.1866 - 26.4548 -2.53532 0 - 27.37 - 34.041 - 32.6758 - 11.75 - 10.8416 -9.37385 0 - 29.243 0 - 48.87 0 1024.236 Infinity 608.5712 2534.683 Infinity Infinity 0 41.84552 19.9601 16.993 11.50722 37.096 12.01538 23.00434 116.4478 79.923 68.822 54.94591 22.44298 12.20215 12.84913 10 0 0 0 10 20 50 20 20 10 20 019 0 44.95 0 2.20215 0 C20 C21 10 10 A linear programming software shows the following solution: Click the icon to view the data concerning products. Click the icon to view the data concerning constraints. nonbinding a) Only product A158 is not produced. binding b) Clearly explain the meaning of each shadow price. Since the shadow price for constraints Cz, C5, C5, C. C1. Ctg and Co is 0, these are constraints. Click to select your answer(s) and then click Check