Question

Consider this linear optimization problem:

maximize  4 x + 5 y + 6 z

subject to

3 x + 2y <= 100

y + 3 z <= 120

4 x + z <= 80

x, y, z should be non-negative.

Solve this and write down the value of x in the optimal solution.

Answer 1

Taking data into Excel as shown below. Formulas used are:- F3 = C3*C6+03*06+ E34E6 , similarly for fulfs CO = 264C8+ DEED8+ EGTES Going to Data - Solver l entering valves as Shown below. Clicking Solve, we get the optimal solution as shown below. .

B E F G H Solver Parameters Used RHS Set Objective: $C$10 Units X Constr 1 Constr 2 OPNI 5 <= 4. 5<= 100 120 To: Max Min Value Of: 0 80 By Changing Variable Cells: $C$6:$E$6 Variables Subject to the Constraints: $F$3:5F55 <= $H$3:SH$5 Obj coeff Add Change 10 Obj value] Delete Reset All Load/Save Make Unconstrained Variables Non-Negative Select a Solving Method: Simplex LP Options Solving Method Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear. Select the LP Simplex engine for linear Solver Problems, and select the Evolutionary engine for Solver problems that are non- smooth. Close Solve

в с D E F RHS Units X Constr 1 Constr 2 100 Iz Used 20 100 <= 13 120 <= 1 23.33333 <= 50 23.333333 120 80 Variables Obj coeff 4 5 6 Obj value 390