This is probably a discretionary purchase. Discretionary income is a person's money after all essentials have been paid. It's the money a person would use on anything that is not necessary (ie. rent/house payment, food, electric, heat, etc.).
When we change the coefficients of the variables in the objective function, the optimal solution may or may not change as the weights (coefficient) are different for each constraints for both the variabls. So, it all depends on the coefficient of the variables in the constraints.
In this case, the optimal solution does not change on changing the coefficient of X from 8 to 6 in the objective function.
The critical region would remain same (as shown below) as it is defined by the constraints and not the objective function.
(0,9) (0,5) (0,3) (0,0) (3,0) (5,0) (9,0) The feasible region is shown in white
However, the optimal value of the objective function would change as shown below-
Vertex Lines Through Vertex Value of Objective
(3,2) x+3y = 9; 2x+2y = 10 42
(9,0) x+3y = 9; y = 0 54
(2,3) 2x+2y = 10; 6x+2y = 18 48
(0,9) 6x+2y = 18; x = 0 108
So, we can see that the minimum value now has become 42 (which had to change obviously).
So, the new critical points are (4,12), (4,24), (8,24) and (8,12).
So, the values of the objective function at these points can be calculated as -
Vertex Value of Objective
(4,12) 8*4+12*12 = 176
(4,24) 8*4+12*24 = 320
(8,24) 8*8+12*24 = 352
(8,12) 8*8+12*12 = 208
So, the new optimal solution is (4,12) and the optimal value is 176.
if we knew the range of the variables in the part B and C earlier, we could have just said that the optimal solution will not change as the value would have been no longer depended on the coefficients of variables in the constraints.
<span>In a database with thousands of products, how would you find a certain product number? Depending on how the database is organized you should be able to search for a certain product/product number by putting in the same, then quantity the product is sold as, where the product was made, or a description. There are a few ways a company could have their database organized so it is important to make sure you are searching the database how they have it set up. </span>