Linear Programming in relationship to the Profit Maximization of the Math Problem

Linear Programming in relationship to the Profit maximisation of the Business - Math Problem ExampleDx=yCA2x+3y=30B x + y = 10500000The feasibility bea would be the region with boundaries ray BC, ray AD and segment AB. The co-ordinates of A and B are (5250000, 5250000) and (6, 6) respectively. The encourage of the objective guide at these points is 0.45 X 5250000 = 2362500 and 2.7 respectively. The evaluate of the objective function at the points of ray AD beyond point A would be 0.2x + 0.25(10500000 - x) i.e. 2625000 - 0.05x and this valuate go forth be maximum when 0.05x is minimum i.e. when x=0 as we cannot take x as negative since x is the value of new houses and this maximum value of 2625000 testament be attained at point D. Similarly the value of objective function on ray BC beyond points B is 0.2x + 0.25(30-2x)/3 i.e. 2.5 +0.03x and this will be maximum when x is maximum i.e. at point B itself. then the maximum value of amplification in this case is at point D i.e. 2625000 and it is more than that in the earlier case. Therefore at that place would be make up in the profit of 2625000-2624999.8=0.2 million.b)would it be worthwhile increase the skilled workforce The cost of taking an another skilled laborer is 15000. reckon there are 181 laborers instead of 180. then the simplicity line BC on page two will be shifted right. The co-ordinates of B and C will be (4, 7.38) and (9.083, 4) and the values of the objective function at B and C will be 2.645 and 2.8166 respectively. This room at point C there will be increase in profit of 16000 which would protract up the overhead of additional laborer of 15000. So, I think it is worthwhile increasing the skilled workforce.c)would the optimal solution change if the profit contributions...2625000 - 0.05x and this value will be maximum when 0.05x is minimum i.e. when x=0 as we cannot take x as negative since x is the value of new houses and this maximum value of 2625000 will be attained at point D. Simi larly the value of objective function on ray BC beyond points B is 0.2x + 0.25(30-2x)/3 i.e. 2.5 +0.03x and this will be maximum when x is maximum i.e. at point B itself. Thus the maximum value of profit in this case is at point D i.e. 2625000 and it is more than that in the earlier case. Therefore there would be increase in the profit of 2625000-2624999.8=0.2 million.Suppose there are 181 laborers instead of 180. then the constraint line BC on page two will be shifted right. The co-ordinates of B and C will be (4, 7.38) and (9.083, 4) and the values of the objective function at B and C will be 2.645 and 2.8166 respectively. This means at point C there will be increase in profit of 16000 which would cover up the overhead of additional laborer of 15000. So, I think it is worthwhile increasing the skilled workforce.Suppose the profit contributions are 19% and 26% respectively and that the objective function is 0.19x + 0.26y and the value of objective function at point A on page 2 will be 2729999.72 i.e. there will be increase. If we just interchange the profit contributions i.e.