Mathematical modeling

Profit produced from each 240-m 2 home = LE 18,000Maximum fund available for construction = LE 500,000One-third of the hoses should be from the 240-m 2 type.Maximize 15000x 1 + 18000x 2Subject to 6000x 1 + 9000x 2 ≤ 450000x 2 ≥ 0.33(x 1 + x 2 ) or -0.33x 1 + 0.67x 2 ≥ 0x 1 , x 2 ≥ 0As shown in the following figure, the number of 200-m 2 homes is 43 homes, while thenumber of 240-m 2 home is 21 homes, which satisfies a maximum profit of LE 1,029,399.15000x 1 + 18000x 2 = 10293996000x 1 + 9000x 2 ≤ 450000Feasible regionOptimum solution(43.13, 21.24)-0.33x 1 + 0.67x 2 ≥ 02.8.3 Example 3Resolve example 2.8.2 using the Solver program of Excel.SolutionFirst, set the modelin Excel spreadsheetprogram as follow:The solution is shown in the following figure.Systems Analysis 39 Dr. Emad Elbeltagi