please can someone help me to solve this question by determining the optimal solution to be implemented . thanks

Example: A company manufactures two products X and Y, which require, the following resources. The resources are the capacities machines M1, M2, and M3. The available capacities are 50, 25, and 15 hours respectively in the planning period. Product X requires 1 hour of machine M2 and 1 hour of machine M3. Product Y requires 2 hours of machine M1, 2 hours of machine M2 and 1 hour of machine M3. The profit contribution of products X and Y are Rs.5/-and Rs.4/- respectively. In the above problem, Products X and Y are competing candidates or variables. Machine capacities are available resources. Profit contribution of products X and Y are given. Now let us formulate the model. 11 Let the company manufactures x units of X and y units of Y. As the profit contributions of X and Y are Rs.5/- and Rs. 41- respectively. The objective of the problem is to maximize the profit Z, hence the objective function is: Maximize Z = 5x + 4y OBJECTIVE FUNCTION. This should be done so that the utilization of machine-hours by-products x and y should not exceed the available capacity. This can be shown as follows: For Machine M1 Ox + 2ys 50 For Machine M2 1x + 2ys 25 and LINEAR STRUCTURAL CONSTRAINTS. For machine M3 1x + Tys 15 But the company can stop production of x and y or can manufacture any amount of x and y. It cannot manufacture negative quantities of x and y. Hence, we have write, Both x and y are > 0. NON- NEGATIVITY CONSTRAINT