For the following problem

(a) formulate the dual,

(b) Solve the dual, using the simplex algorithm,

(c) Use the final dual tableau to determine the optimal values of the primal objective function and decision variables.

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Minimize subject to (a) Maximize subject to c14y+40y2 + 18y3 2y15y2 y3 50 y+5y2+3y3 30 y1 y2 y30 = 50x1 + 30x2 2x1 + x2 14 5x1 +5x240 x1+3x218 X1, X20 (b) The dual was solved as a primal in Problem 8.1, where the final tableau was = X1 x2 $1 $2 $3 Constant 1 0 1 - 0 6 0 1 -1 0 2 0 0 2 -1 1 6 00 20 2 0 360 (c) The primal decision variables are given by the shadow prices or marginal values of the corresponding resources in the dual which are boxed above for easy identification. Thus, = 20, y2 = 2, 3 = 0, and 14(20) + 40(2) + 18(0) = 360.