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Question 2 of 5 · Linear Programming
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The minimum value of subject to , , , is

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Answer: Option A — 12

Detailed Solution

1

Corner points of the (unbounded) feasible region: (0, 8), (2, 4) and (6, 0).

2

= 24, 16 and 12 respectively.

3

The smallest value is 12. Since is the half-plane on the origin side and has no point in common with the region, 12 is the minimum.

✓ Check

At (6, 0): and , so the point is feasible.

⚠ Common trap

(B) 16 — picks the intersection point (2, 4) as the answer by habit.

Quick tip

Unbounded region: confirm the minimum by checking that misses the region

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Linear Programming — Preparation

This question tests your understanding of Linear Programming, a key topic in the Quantitative Aptitude section. The detailed solution above uses a step-by-step approach to show the reasoning, and where available, a shortcut that helps you solve similar questions in under 90 seconds during the actual exam.

Linear programming (LPP) is a method for finding the best outcome, such as maximum profit or minimum cost, subject to a set of linear constraints. A linear programming problem has an objective function to maximise or minimise, decision variables, and constraints written as linear inequalities, along with the condition that the variables are non-negative. In MHT CET, problems are solved graphically. Draw each constraint as a line, shade the region that satisfies all the inequalities (the feasible region), and find its corner points. The optimal value of the objective function always occurs at one of these corner points, so evaluate the objective function at each one and choose the largest or smallest value. Questions also ask you to form the LPP from a word problem, identify the feasible region from a graph, or recognise when a problem has no feasible solution or an unbounded one. Practise the linear programming questions below, each with a step-by-step graphical solution.

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