Consider a LPP with objective function $Z = px + qy$ subjected to certain constraints with a bounded feasible region such that maximum $Z = 80$ and minimum $Z = 52$, which occur at the corner points $(0, 8)$ and $(2, 4)$ respectively, Then the value of $p+q$ is:

A manufacturer of electronic circuit has a stock of 200 resistors, 120 transistors and 150 capacitors and is required to produce two types of circuits A and B. Type A requires 20 resistors, 10 transistors and 10 capacitors. Type B requires 10 resistors, 20 transistors and 30 capacitors. If the profit on type A circuit is Rs. 50 and that on type B circuit is Rs. 60, identify the constraints for this LPP, if it was assumed that x circuit B of type A and y circuits of type B was produced by the manufacturer.

A. $x + 2y \geq 15$

B. $2x + y \leq 20$

C. $x + 2y \leq 12$

D. $x, y \leq 0$

Choose the correct answer from the options given below

The feasible region for a LPP is shown in the given figure. The maximum value of $z = 2x + 5y$ is :

The linear constraints for which the shaded region in the figure are:

The corner points of the bounded feasible region for an LPP are: (5, 5), (15, 15), (0, 20) and (0, 10). Let $z = 3x + 9y$ be the objective function. Then the value of $maximum(z) - minimum(z)$ is

A person wants to invest an amount of ₹ $75,000$. He has two options A and B yielding $8 \%$ and $9 \%$ return respectively on the invested amount. He plans to invest at least ₹ $15,000$ in Plan A and at least ₹ $25,000$ in Plan B. Also he wants that his investment in Plan A is less than or equal to his investment in Plan B. Which of the following options describes the given LPP to maximize the return (where $x$ and $y$ are investments in Plan A and Plan B respectively) ?

The corner points of the bounded feasible region determined by the system of linear constraints of an LPP are (0, 0), (0, 8), (5, 0) and (4, 10). Let $z = 3x - 4y$ be the objective function, then the minimum value of $z$ is: