The correct answer is: C. both (a) and (b).
Linear programming is a mathematical method for finding the best (optimum) solution to a problem in a way that satisfies a set of linear constraints. The constraints can be on the quantities of resources that are available, the quantities of products that can be produced, or the costs or profits that can be incurred.
The optimum solution is the one that maximizes the profit or minimizes the cost, subject to the constraints. Linear programming can be used to solve a wide variety of problems, including production planning, transportation scheduling, and financial planning.
Option A is correct because linear programming can be used to identify the optimum quantities of the variables. The optimum quantities are the ones that maximize the profit or minimize the cost, subject to the constraints.
Option B is also correct because linear programming can be used to identify the maximum profit or minimum cost that can be expected. The maximum profit or minimum cost is the one that is achieved when the optimum quantities of the variables are used.
Option C is the correct answer because it includes both Option A and Option B.
Option D is incorrect because linear programming can be used to identify both the optimum quantities of the variables and the maximum profit or minimum cost.
Option E is incorrect because linear programming is a mathematical method that can be used to solve a wide variety of problems.