maximise p=15x+10y
To maximize the objective function p = 15x + 10y, where x and y are variables, you will need to find the values of x and y that yield the highest possible value for p.
There are different methods to solve this problem, but one common approach is to use linear programming. Linear programming is a mathematical technique used to find the maximum or minimum of a linear objective function subject to linear equality and inequality constraints.
To solve this problem using linear programming, follow these steps:
1. Identify any constraints or limitations. In this case, there might be constraints or limitations on the values of x and y. For example, x and y might need to be non-negative (x, y ≥ 0), or there might be upper or lower bounds on their values. Let's assume there are no constraints for now.
2. Define the variables. In this case, we already have the variables x and y.
3. Formulate the objective function. We want to maximize p = 15x + 10y.
4. Formulate any constraints. If there are any constraints, such as x + y ≤ 10 or x ≥ 2, include them in the problem formulation. If there are no constraints, proceed to the next step.
5. Use a linear programming solver to solve the problem. Linear programming solvers can be found in various mathematical software packages or online optimization tools. Enter the objective function and constraints (if any) into the solver, and let it find the optimal solution.
6. Interpret the solution. The solver will provide a solution that maximizes the objective function p. The solution will provide the values of x and y that yield the maximum value for p.
In summary, to maximize p = 15x + 10y, you can use linear programming to find the optimal values of x and y. Consider any constraints or limitations on the variables and use a linear programming solver to obtain the optimal solution.