This example was found on linkedIn SlideShare **Page 5**:

**Pancakes**

3 cups Bisquick

1 cup Milk

2 Eggs

**Serves 6 **

**Waffles**

2 cups Bisquick

2 cups Milk

2 Eggs

**Serves 5**

You have 24 cups of Biquick, 18 cups of milk, and 20

eggs. If you want to **feed as many people as possible**,

how many batches of each should you make?

p = number of batches of pancakes

w = number of batches of waffles

**Optimisation equation: S(Servings)**

S = 6 * p + 5 * w

**Subject to:**

3 * p + 2 * w <= 24 cups of Bisquick

1 * p + 2 * w <= 18 cups Milk

2 * p + 2 * w <= 20 Eggs

**Also written as:**

p = 3 * p + 2 * w

q = 1 * p + 2 * w

r = 2 * p + 2 * w

-inf < p <= 24 0 <= x1 < +inf

-inf < q <= 18 0 <= x2 < +inf

-inf < r <= 20 0 <= x2 < +inf

// Philipp Siedler // Linear Programming // Real Life Example 2 #include <stdio.h> #include <stdlib.h> #include <glpk.h> #include <std_lib_facilities.h> int main(void) { glp_prob *lp; int row_index[1 + 1000]; //Row indices of each element int col_index[1 + 1000]; //column indices of each element double value[1 + 1000]; //numerical values of corresponding elements double z, x1, x2, x3; lp = glp_create_prob(); //creates a problem object glp_set_prob_name(lp, "sample"); //assigns a symbolic name to the problem object glp_set_obj_dir(lp, GLP_MAX); //calls the routine glp_set_obj_dir to set the //omptimization direction flag, //where GLP_MAX means maximization //ROWS glp_add_rows(lp, 3); //adds three rows to the problem object //row 1 glp_set_row_name(lp, 1, "p"); //assigns name p to first row glp_set_row_bnds(lp, 1, GLP_UP, 0.0, 24.0); //sets the type and bounds of the first row, //where GLP_UP means that the row has an upper bound. //-inf < p <= 24 //row 2 glp_set_row_name(lp, 2, "q"); //assigns name q to second row glp_set_row_bnds(lp, 2, GLP_UP, 0.0, 18.0);//-inf < q <= 18 //row 3 glp_set_row_name(lp, 3, "r"); //assigns name r to second row glp_set_row_bnds(lp, 3, GLP_UP, 0.0, 20.0);//-inf < r <= 20 //COLUMNS glp_add_cols(lp, 2); //adds three columns to the problem object //column 1 glp_set_col_name(lp, 1, "x1"); //assigns name x1 to first column glp_set_col_bnds(lp, 1, GLP_LO, 0.0, 0.0); //sets the type and bounds to the first column, //where GLP_LO means that the column has an lower bound glp_set_obj_coef(lp, 1, 6.0); //sets the objective coefficient for thr first column //S = 6 * p + 5 * w //column 2 glp_set_col_name(lp, 2, "x2"); //assigns name x2 to first column glp_set_col_bnds(lp, 2, GLP_LO, 0.0, 0.0); //sets the type and bounds to the second column glp_set_obj_coef(lp, 2, 5.0); //sets the objective coefficient for thr second column /* p = 3 * p + 2 * w q = 1 * p + 2 * w r = 2 * p + 2 * w */ row_index[1] = 1, col_index[1] = 1, value[1] = 3.0; // a[1,1] = 100000.0 row_index[2] = 1, col_index[2] = 2, value[2] = 2.0; // a[1,2] = 200000.0 row_index[3] = 2, col_index[3] = 1, value[3] = 1.0; // a[1,2] = 200000.0 row_index[4] = 2, col_index[4] = 2, value[4] = 2.0; // a[2,1] = 100.0 row_index[5] = 3, col_index[5] = 1, value[5] = 2.0; // a[2,2] = 75.0 row_index[6] = 3, col_index[6] = 2, value[6] = 2.0; // a[2,2] = 75.0 for (int i = 1; i < 7; i++) { cout << value[i]; cout << ((i % 2 == 0) ? "\n" : "\t"); } glp_load_matrix(lp, 6, row_index, col_index, value); //calls the routine glp_load_matrix //loads information from three arrays //into the problem object glp_simplex(lp, NULL); //calls the routine glp_simplex //to solve LP problem z = glp_get_obj_val(lp); //obtains a computed value of the objective function x1 = glp_get_col_prim(lp, 1); //obtain computed values of structural variables (columns) x2 = glp_get_col_prim(lp, 2); //obtain computed values of structural variables (columns) printf("\nServings(z) = %g; pancakes(x1) = %g; waffles(x2) = %g;\n", z, x1, x2); //writes out the optimal solution glp_delete_prob(lp); //calls the routine glp_delete_prob, which frees all the memory keep_window_open(); //leave this line out and run program with ctrl + F5 to keep window open //that means you won't need std_lib_facilities.h }

Output:3 2 1 2 2 2 GLPK Simplex Optimizer, v4.63 3 rows, 2 columns, 6 non-zeros * 0: obj = -0.000000000e+00 inf = 0.000e+00 (2) * 2: obj = 5.400000000e+01 inf = 0.000e+00 (0) OPTIMAL LP SOLUTION FOUND Servings(z) = 54; pancakes(x1) = 4; waffles(x2) = 6; Please enter a character to exit