Embibe Experts Solutions for Exercise 2: Assignment

Let $X_1$ and $X_2$ are optimal solutions of a $\mathrm{LPP}$ for which objective function is maximum. Then

We have to purchase two articles $A$ and $B$ of cost $\mathrm{Rs} 45$ and $\mathrm{Rs} 25$ respectively. I can purchase total article maximum of $\mathrm{Rs} 1000$ . After selling the articles $A$ and $B$ the profit per unit is $5$ and $\mathrm{Rs} 3$ respectively. If I purchase $x$ and $y$ number of articles $A$ and $B$ respectively, then the mathematical formulation of problem is

A company manufactures two types of products $A$ and $B$. The storage capacity of its godown is 100 units. Total investment amount is $\mathrm{Rs} 30,000$. The cost price of $A$ and $B$ are $\mathrm{Rs} 400$ and $\mathrm{Rs} 900$ respectively. If all the products have sold and per unit profit is $\mathrm{Rs} 100$ and $\mathrm{Rs} 120$ of $A$ and $B$ respectively. If $x$ units of $A$ and $y$ units of $B$ be produced, then the mathematical formulation of problem is

Which of the following system of equations is represented by the shaded portion of the graph given below?

An owner of a lodge plans an extension which contains not more than 50 rooms. At least 5 must be executive single room. The number of executive double rooms should be at least 3 times the number of executive single rooms. He charges Rs 3000 for executive double room and Rs 1800 for executive single room per day. The linear programming problem to maximize the profit if $x_1$ and $x_2$ denote the number of executive single rooms and executive double rooms respectively, is

Minimize $Z=\sum _{j=1}^{10}\sum _{i=1}^{30}{C}_{ij}·X_{ij}$
subject to
$\sum _{j=1}^{10}{X}_{ij}\le a_{i,}i=1,2,3....30$

$\sum _{i=1}^{30}{X}_{ij}\le b_{j,}j=1,2,3....10$
is a $\mathrm{LPP}$ with number of constraints

If Salim drives a car at a speed of $60 \mathrm{km}/\mathrm{h}$, he has to spend Rs $5$  per $\mathrm{km}$ on petrol. If he drives at a faster speed of $90 \mathrm{km}/\mathrm{h}$, the cost of petrol increases to Rs $8$ per $\mathrm{km}$. He has Rs $600$ to spend on petrol and wishes to travel the maximum distance within an hour. If $x_1$ and $x_2$ denote the distance (in km) travelled at a speed of $60 \mathrm{km}/\mathrm{h}$ and $90 \mathrm{km}/\mathrm{h}$ respectively, then the linear programming problem is

For the $\mathrm{LPP}$, minimize $Z=2 x+y$ subject to $x+2y\le 10,x+y\ge 1,y\le 4$ and $x,y\ge 0$, then $Z$ is