Consider the following Linear Programming Pro blem:

BZ Chemicals blends its private label orchard spray from four individual compounds. Management would like to make the blend at as low a cost as possible while maintaining the requirements for chemical structure. The following linear programming problem has been formulated.

Let Xi= amount of compound i in the blend, i = 1,...,4

Minimize 23Xl+35X2+20X3+4X4

Subject to 13Xl+8X2+12X3+7X4 >= 800 Units of Chemical 1 6X1 +20X2+18 X3+11.2 X4 >,. 950 Units of Chemical 2 Xl , X2,X3, and X4>=0

Answer the following questions using the attached LP Computer Output:

1. What costs would each of the non-used compounds have to have in order to be used in the blend?
2. What would happen if compound 1 cost 30?

LINEAR PROGRAMMING PROBLEM MIN 23X1+35X2+20x3+4x4 S.T. 1) 2) 13X1+8X2+12X3+7X4>800 6X1+20X2+18X3 +11.2X4 >950 OPTIMAL SOLUTION Objective Function value = 457.143 Variable Value Reduced Costs X1 X2 X3 0.000 0.000 0.000 114.286 15.571 30.429 13.143 0.000 X4 Constraint slack/Surplus Dual Prices 1 2 0.000 330.000 -0.571 0.000 Current Value OBJECTIVE COEFFICIENT RANGES variable Lower Limit x1 7.429 4.571 X3 6.857 X4 0.000 X2 23.000 35.000 20.000 4.000 Upper Limit No Upper Limit No Upper Limit No Upper Limit 11.667 RIGHT HAND SIDE RANGES Constraint Lower Limit Current Value Upper Limit 1 2 593.750 No Lower Limit 800.000 950.000 No Upper Limit 1280.000