Jamia Millia Islamia Linear Programming Previous Year Questions (PYQs)
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In mathematical programming, goals represented by objective functions include
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Solution
Objective functions can represent any of these based on problem type.
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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Solution
$2x + 3y = 77,\ 3x + 2y = 73$ → solving gives $x = 17,\ y = 13.$
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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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.
$Z = 7x + y$, 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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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 $(0,5)$
Objective of linear programming for an objective function is to......
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Solution
In linear programming, the main goal is to maximize or minimize an objective function
subject to a set of linear constraints.
The objective function of a linear programming problem is
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Solution
In linear programming, the objective function represents the quantity (profit, cost, etc.) to be maximized or minimized, subject to given constraints.
Linear programming model which involves funds allocation of limited investment is classified as
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Solution
This model selects projects under limited funds for maximum return. It is known as a capital budgeting model.
According to system of constraints, solution set graphical representation is classified as
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Solution
The intersection of all constraints forms the feasible region, which represents all possible solutions.
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