Mann Enterprises is a Houston manufacturer of tables and accessories for personal computers. The…

Mann Enterprises is a Houston manufacturer of tables and accessories for personal computers. The company is caught in a vicious cross fire 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 firm 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 (f). Steel Alloy Required (Lb.) Plastic Required (Sq. Ft.) 0.4 0.5 Minimum Monthly Demand (Units) Formica Required (Bd. Ft.) 10.9 Aluminum Required (Lb.) 5.8 10.3 1.1 2.0 Wood Required (Bd. Ft.) 0.7 1.8 1.5 2.0 1.2 1.5 7.0 5.0 4 6 10 12 Labor Required (Hr.) 3.1 1.0 1.2 4.8 5.5 0.8 2.3 20 10 10 Product A158 B179 C023 D045 E388 F422 G366 H600 1701 J802 K900 L901 M050 N150 P259 Availability 9.1 10 5 0.4 1.2 1.4 1.4 1.0 0.4 0.3 ? ?? | N | ? ? | 01 8.1 7.1 6.2 7.3 10.0 11.0 12.5 13.1 4.9 10.0 11.1 12.4 5.2 6.1 7.7 5.0 2.1 Contribution to Profit $18.79 6.31 8.19 45.88 63.00 4.10 81.15 50.06 12.79 15.88 17.91 49.99 24.00 88.88 77.01 1 Il 20 10 20 50 20 20 10 20 10 10 4.8 1.9 1.4 1.0 5.1 3.1 7.7 6.6 0.2 2 1.8 2.7 1.1 1.5 5.0 5.8 6.2 10 15.0 1.0 980 400 600 2,500 1,800 1,000 per month 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 Z = 18.79XA+ 6.31X8 + 8.19Xc + 45.88Xp + 63.00XE +4.10X: + 81.15X6 + 50.06X4 + 12.79X, + 15.88X, + 17.91 XK+ 49.99 XL + 24 XM + 88.88 XN+ 77.01 Xp Constraints (enter your responses as whole numbers): Constraints (enter your responses as whole numbers): Material constraints: Steel Alloy (C1) 4X8 +6Xc + 10XD + 12XE + 10XG + 5X + X1 + X; + 2XL + 10Xx + 10Xp Plastic (C2) .4XA+.5X8 + .4Xp + 1.2XE + 1.4XF + 1.4X6 + 1.0XH +.4X, + .3X; + 2XK+ 1.8X_ + 2.7XM + 1.1XN Wood (C3) .7XA + 1.8X8 + 1.5Xc + 2.0Xp + 1.2XE + 1.5XF + 7.0XG +5.0XH + 1.5XL + 5.0XM + 5.8Xn+6.2Xp Aluminum (C4) 5.8XA+ 10.3X3 + 1.1Xc + 8.1XE + 7.1XF+6.2XG +7.3X4+ 10.0X, + 11.0X; + 12.5Xk+ 13.1X + 15.0Xp Formica (C5) 10.9XA + 2.0X8 + 2.3Xc + 4.9X€ + 10.0XF + 11.1XG + 12.4X4 +5.2X, + 6.1X, +7.7XK + 5.0XL + 2.1XM+ 1.0XP Labor constraint (C6): 3.1XA+ 1.0X8 + 1.2Xc + 4.8Xp + 5.5XE +.8XF+ 9.1X6 + 4.8XH +1.9%,+ 1.4X;+ 1.0Xk+5.1X2 + 3.1XM + 7.7Xx + 6.6Xp Minimum demand constraints: (C7): XA20 (C10): XD 10 (C13): XG 2 10 (C16): X, 220 (C19): XM (Cg): X8 220 (C1): XE 20 (C14): XH 2 20 (C17): XK 220 (C20): XN (C9): Xc 2 10 (C12): XF 2 20 (C15): X, 250 (C18): XL 2 10 (C21): Xp Constraints (enter your responses as whole numbers): Material constraints: Steel Alloy (C1) 4X8 + 6Xc + 10XD + 12XE + 10XG + 5XH + X1 + X; + 2X[ + 10XN + 10XP 1.0XH Plastic (C2) .4XA+.5X8+ .4X0 + 1.2XE + 1. +.4X, +.3X;+.2Xk+1.8XL + 2 :+ 7.0XG Wood (C3) .7XA + 1.8X8 + 1.5Xc + 2.0X + + 5.0X4+ 1.5XL +5.0Xm + 5.8X XG Aluminum (C4) 5.8XA + 10.3X8 + 1.1Xc + 8.1X +7.3XH + 10.0x, + 11.0X, + 12. = + 15.0Xp < Formica (C5) 10.9XA + 2.0X8 + 2.3Xc +4.9%, + 12.4X4 + 5.2X, +6.1X, + 7.7) 1.1XG 1XM + 1.0XP Labor constraint (C6): 3.1XA+ 1.0X8 + 1.2Xc + 4.8XD + 9.1X6 + 4.8XH +1.9%, + 1.4X; + 1.0XK + 5.1X_ + 3.1XM + 7.7XN + 6.6Xp Minimum demand constraints: (C7): XA20 (Co): Xp> 10 (C13): XG 2 10 (C16): X, 220 (C19): XM (Cp): X8 220 (C11): XE 20 (C14): XH 220 (C17): XK 220 (C20): XN (Cg): Xc 2 10 (C12): XF2 20 (C15): X, 250 (C18): XL 2 10 (C21): Xp