Consider the following linear program and its LINDO output. The variables x, y a

Question

Consider the following linear program and its LINDO output. The variables x, y and z are product types 2x 3y52 Material)2x y 5z 20 Labor) 3x2y5z 35 LINDO output OBJECTIVE FUNCTION VALUE 1) 20.00000 VARIABLE VALUE REDUCED COST 10.000000 0.000000 0.000000 0.000000 4.00000 0.000000 SLACK OR SURPLUS RON MATERIAL) LABOR) 0.000000 5.000000 DUAL PRICES 1.000000 0.000000 NO.ITERATIONS RANGES IN WHICH TRE BASIS IS UNCHANGED: VARIABLE OBJ COEFFICIENT RANGES ALLOWABLE ALLONABLE CURRENT COEF 2.000000 3.000000 5.000000 INCREASE DECREASE INFINITY 4.000000 0.000000 0.000000 INFINITY INFINITY RON MATERIAL LABOR RIGHTHAND SIDE RANGES ALLOKABLE INCREASE 3.333333 ALLONABLE DECREASE 20.000000 CURRENT RHS 20.000000 35.000000 INFINITY 5.000000 -LINDO output end

Explanation / Answer

A.

The Reduced Cost tells us the amount by which the objective function coefficient for the variable has to be changed before that variable becomes non-zero

So by this, the price of y should be should be increased by 4 to make the value of y greater than zero or a minimum of 1 unit

Objective function

2x+3y+5z

From objective function price of Y=3

So m he price must be at least ( 3+4=7) 7, to produce at least 1 unit of y

B.

The new optimal solution remains the same .x-10,y-0,z-0

C.

There is at least one another optimal solution if

Z has an optimal value of 0 and A reduced cost of 0. Hence there must be at least one more optimal solution

D.

Resource material has a dual/shadow price of 1 and no slack. Hence this is the resource that is most sensitive to change

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