2 A company produces two models of a product X and Y A linea

2. A company produces two models of a product, X and Y. A linear programming model is used to determine the production schedule. The formulation is as follows: (15 Points) Maximize Profit: 50X + 60Y Constraints: 8X + 10Y < 800 X + Y < 120 4X + 5Y < 500

c. How much could the profit change on X without changing the values of X and Y in the optimal solution?

Solution

the constriant of the above prooblem is

4x+5y<500.............1)

792X-9y<120 ............2)

792x-9y>0......................3)

solby solving 1 and 2nd equation

36x +45y<4500 (multiply equation 1 by 9).............................eq 4)

3960x-45y<600 (multiply equation 2 by 5).............................eq 5)

3996x< 5100 ( add 4 and 5 eqaution together)

x<1.276276

from equatiopn 4 36*1.276276+5y<500

y<98.97898

put value of x and y in eqaution 3

792*1.276276 -9*98.9789

=119.9315 which is greaterr than 0

This means third constraint is alos satisfied if x= 1.276276 and y= 98.978978

Therfore profit change in x = 1.276276