Question

Solve the linear programming problem

Answer 1

After solving the linear programming problem, we get the answer as 250.

What is linear programming?

When a linear function is exposed to multiple restrictions, linear programming maximizes or minimizes the function. This method determines the best way to use the resources that are currently available and aids managers in using the process to make decisions about the most efficient use of scarce resources, such as money, time, materials, and machinery. Linear programming has been useful for guiding quantitative decisions in business planning, industrial engineering, and—to a lesser extent—in the social and physical sciences.

Solution explained:

$\left \{ {{2x + y = 12} \atop {x + y = 7}} \right.$            x=3, y=4    P(3,4)       Coordinates of the solution point

$\left \{ {{x + y = 7} \atop {x + 2y = 10}} \right.$            x=4, y=3    Q(4,3)      

                                                           Coordinates of the simultaneous eqs.

$\left \{ {{2x + y = 12} \atop {x + 2y = 10}} \right.$            x=14/3, y=8/3

Putting the values of x and y in the equation P = 30x + 40y and calculating we get

P(P) = 250, P(Q) = 240, P(R) = 246.67

So, the answer is 250

To learn more about linear programming, use the link given
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