1. Kelly Industries manufactures two different structural support products used in the construction of large boats and ships. The two products Z345 and W250 are coming in two grades, standard and industrial. Two specialty treated materials are used in the production process - zinc and iron. Kelly nets a profit of $400 on each standard Z345 and $500 on each standard W250. Industrial models net a 40% premium over the standard models. Each week up to 2500 pounds of zinc and 2800 pounds of iron are available. The following table gives the per unit requirements (in pounds) for each model. Z345 W250 Materi Standar Industri Standar Industri a d al d al Zinc 25 46 16 34 Iron 50 30 28 12 Kelly has a contract to provide 20 units of both standard and industrial Z345 combined but can sell any additional amount produced. Company policy mandates that at least 50% of the production must be industrial models and that neither Z345 nor W250 can account for more than 75% of the total production. The following linear programming model was formulated to provide the optimal manufacturing plan: X1 and X2 - number of standard and industrial Z345s; Same for Xs and X4 for W250 MAX Profit 400X, + 560X2 + 500X3 + 700X4 S.T. 25X1+ 46X2+ 16X3 + 34X4 2500 (zinc) 50X1 + 30X2+ 28X3+ 12X4 2800 (iron) X1+ X2 2 20 (required Z345's) X2 + X4 0.5(X1+X2+X3+X4) (Industrial mini X1+ X2 0.75(X1+X2+X3+X4) (Max Z345's) X3 + X4 0.75(X1+X2+X3+X4) (Max N250's)