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Jamia Millia Islamia Previous Year Questions (PYQs)

Jamia Millia Islamia Linear Programming PYQ

Jamia Millia Islamia PYQ
In mathematical programming, goals represented by objective functions include





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Jamia Millia Islamia Previous Year PYQ Jamia Millia Islamia JAMIA MILLIA ISLAMIA MCA 2018 PYQ

Solution

Objective functions can represent any of these based on problem type.
Jamia Millia Islamia PYQ
Two bus tickets from city A to B and three tickets from A to C cost Rs. 77, but three tickets from A to B and two tickets from A to C cost Rs. 73. What are the fares for cities B and C from A?





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Jamia Millia Islamia Previous Year PYQ Jamia Millia Islamia JAMIA MILLIA ISLAMIA MCA 2018 PYQ

Solution

$2x + 3y = 77,\ 3x + 2y = 73$ → solving gives $x = 17,\ y = 13.$
Jamia Millia Islamia PYQ
Every gram of wheat provides $0.1$ gram of proteins and $0.25$ gram of carbohydrates. The corresponding values of rice are $0.05$ gram and $0.5$ gram respectively. The minimum daily requirements of proteins and carbohydrates for an average child are $50$ gram and $200$ gram respectively. Then in what quantities wheat and rice be mixed in daily diet to provide minimum daily requirement of proteins and carbohydrates at minimum cost?





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Jamia Millia Islamia Previous Year PYQ Jamia Millia Islamia JAMIA MILLIA ISLAMIA MCA 2023 PYQ

Solution

Let $x =$ grams of wheat and $y =$ grams of rice. Protein constraint: $0.1x + 0.05y = 50$ Carbohydrate constraint: $0.25x + 0.5y = 200$ Simplify: $2x + y = 1000$ $x + 2y = 800$ Solving the two equations gives: $x = 400,\ y = 200.$ Hence, wheat = $400$ g, rice = $200$ g.
Jamia Millia Islamia PYQ
$Z = 7x + y$, subject to constraints: $5x + y \ge 5,\ x + y \ge 3,\ x \ge 0,\ y \ge 0.$ Then minimum value of $Z$ occurs at –





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Jamia Millia Islamia Previous Year PYQ Jamia Millia Islamia JAMIA MILLIA ISLAMIA MCA 2023 PYQ

Solution

Solution: Corner points by solving the constraints: $(0,5),\ (3,0),\ \left(\frac{1}{2},\frac{5}{2}\right)$ Now compute $Z = 7x + y$: At $(0,5): Z = 5$ At $(3,0): Z = 21$ At $\left(\frac{1}{2},\frac{5}{2}\right): Z = \frac{7}{2} + \frac{5}{2} = 6$ Minimum $Z = 5$ at $(0,5)$
Jamia Millia Islamia PYQ
Objective of linear programming for an objective function is to......





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Jamia Millia Islamia Previous Year PYQ Jamia Millia Islamia JAMIA MILLIA ISLAMIA MCA 2020 PYQ

Solution

In linear programming, the main goal is to maximize or minimize an objective function subject to a set of linear constraints.
Jamia Millia Islamia PYQ
The objective function of a linear programming problem is





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Jamia Millia Islamia Previous Year PYQ Jamia Millia Islamia JAMIA MILLIA ISLAMIA MCA 2024 PYQ

Solution

In linear programming, the objective function represents the quantity (profit, cost, etc.) to be maximized or minimized, subject to given constraints.
Jamia Millia Islamia PYQ
Linear programming model which involves funds allocation of limited investment is classified as





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Jamia Millia Islamia Previous Year PYQ Jamia Millia Islamia JAMIA MILLIA ISLAMIA MCA 2018 PYQ

Solution

This model selects projects under limited funds for maximum return. It is known as a capital budgeting model.
Jamia Millia Islamia PYQ
According to system of constraints, solution set graphical representation is classified as





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Jamia Millia Islamia Previous Year PYQ Jamia Millia Islamia JAMIA MILLIA ISLAMIA MCA 2018 PYQ

Solution

The intersection of all constraints forms the feasible region, which represents all possible solutions.

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