Q#1:

Xi: the proportion of Alloy i,  i=1,2,3,4,5.

Minimize        Z = 17X1 + 12X2 + 18.5X3 + 11X4 + 18X5
subject to
                X1 + X2 + X3 + X4 + X5  = 1    
                0.2X1 + 0.1X2 + 0.5X3 + 0.1X4 + 0.5X5 = 0.3   (lead)
                0.6X1 + 0.2X2 + 0.2X3 + 0.1X4 + 0.1X5 = 0.2   (zinc)
                0.2X1 + 0.7X2 + 0.3X3 + 0.8X4 + 0.4X5 = 0.5   (tin)
                X1, X2, X3, X4, X5 >= 0


Q#2:

Xif : the amount of cargo i (in tons) accepted and distributed to the front compartment;
Xic : the amount of cargo i (in tons) accepted and distributed to the central compartment;
Xir : the amount of cargo i (in tons) accepted and distributed to the rear compartment;
        i = 1, 2, 3, 4.

Maximize        Z = 100(X1f + X1c + X1r) + 140(X2f + X2c + X2r)
                   + 110(X3f + X3c + X3r) + 95(X4f + X4c + X4r)
subject to      
                X1f + X2f + X3f + X4f  <= 8
                X1c + X2c + X3c + X4c  <= 12  (compartment weight capacity)
                X1r + X2r + X3r + X4r  <= 7

                500X1f + 700X2f + 600X3f + 400X4f <= 5000
                500X1c + 700X2c + 600X3c + 400X4c <= 7000  (compartment space capacity)
                500X1r + 700X2r + 600X3r + 400X4r <= 3000

                X1f + X1c + X1r <= 15
                X2f + X2c + X2r <= 9
                X3f + X3c + X3r <= 18  (cargo availability)
                X4f + X4c + X4r <= 10

                Xif, Xic, Xir >= 0,  i = 1, 2, 3, 4.


Bonus:

        Any 2 of the following 3 equations:

        12(X1f + X2f + X3f + X4f) - 8(X1c + X2c + X3c + X4c) = 0
         7(X1f + X2f + X3f + X4f) - 8(X1r + X2r + X3r + X4r) = 0
        12(X1r + X2r + X3r + X4r) - 7(X1c + X2c + X3c + X4c) = 0