Minimize the function Z = x + y

Question

Minimize the function Z = x + y,
Subject to:
x + 3y less than/equal to 15
3x + 2y less than/equal to 17
x – 5y greater than/equal to 0
x, y less than/equal to 0

Answer 1

Result: Solver found a solution. All Constraints and optimality conditions are satisfied.
Solver Engine
Engine: GRG Nonlinear
Solution Time: 0.031 Seconds.
Iterations: 0 Subproblems: 0
Solver Options
Max Time Unlimited, Iterations Unlimited, Precision 0.000001, Use Automatic Scaling
Convergence 0.0001, Population Size 100, Random Seed 0, Derivatives Forward, Require Bounds
Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 1%, Assume NonNegative

Objective Cell (Min)
Cell Name Original Value Final Value
$F$7 x, y less than/equal to 0 2 0


Variable Cells
Cell Name Original Value Final Value Integer
$F$8 x 1 0 Contin
$F$9 y 1 0 Contin


Constraints
Cell Name Cell Value Formula Status Slack
$F$10 x+3y 0 $F$10<=15 Not Binding 15
$F$11 3x+2y 0 $F$11<=17 Not Binding 17
$F$12 x-5y 0 $F$12>=0 Binding 0
$F$8 x 0 $F$8<=0 Binding 0
$F$9 y 0 $F$9<=0 Binding 0

The only answer that was found by Solver is x=0 and y=0 to minimize the function and satisfy the constraints.