NCERT Solutions for Chapter: Linear Programming, Exercise 1: EXERCISE

A company manufactures two types of screws $A$ and $B.$ All the screws have to pass through a threading machine and a slotting machine. A box of Type $A$ Screws required $2$ Minutes on the threading machine and $3$ Minutes on the slotting machine. A box of type $B$ Screws required $8$ Minutes of threading on the threading machine and $2$ Minutes on the slotting machine. In a week, each machine is available for $60$ Hours. On selling these screws, the company gets a profit of Rs.$100$ Per box on type A screws and Rs $170$ Per box on type $B$ Screws.

A company manufactures two types of sweaters: type $A$ and type $B.$ It costs Rs $360$ to make a type $A$ sweater and Rs $120$ to make a type $B$ Sweater. The company can make at most $300$ sweaters and spend at most Rs $72000$ a day. The number of sweaters of type $B$ cannot exceed the number of sweaters of type $A$ by more than $100.$ The company makes a profit of Rs $200$ for each sweater of type $A$ and Rs $120$ for every sweater of type $B.$ Formulate this problem as a $LPP$ to maximise the profit to the company.

A man rides his motorcycle at the speed of $50 \raisebox{1ex}{$\mathrm{km}$}\!\left/ \!\raisebox{-1ex}{$h$}\right..$ He has to spend Rs $2 \mathrm{per} \mathrm{km}$ on petrol. If he rides it at a faster speed of $80 \raisebox{1ex}{$\mathrm{km}$}\!\left/ \!\raisebox{-1ex}{$h$}\right.$, the petrol cost increases to Rs $3 \mathrm{per} \mathrm{km}.$ He has at most Rs $120$ to spend on petrol and one hour’s time. He wishes to find the maximum distance that he can travel. Express this problem as a linear programming problem.

A company manufactures two types of screws $A$ and $B.$ All the screws have to pass through a threading machine and a slotting machine. A box of Type $A$ screws requires $2$ minutes on the threading machine and $3$ minutes on the slotting machine. A box of type $B$ screws requires $8$ minutes of threading on the threading machine and $2$ minutes on the slotting machine. In a week, each machine is available for $60$ hours. On selling these screws, the company gets a profit of Rs $100$ per box on type A screws and Rs $170$ per box on type $B$ screws. Solve the linear programming problem and determine the maximum profit to the manufacturer.
 

A manufacturer produces two Models of bikes - Model $X$ and Model $Y$. Model $X$ takes a $6$ man-hours to make per unit, while Model $Y$ takes $10$ man-hours per unit. There is a total of $450$ man-hour available per week. Handling and Marketing costs are $₹2000$ and $₹1000$ per unit for Models $X$ and $Y$, respectively. The total funds available for these purposes are $₹80,000$ per week. Profits per unit for Models $X$ and $Y$ are $₹1000$ and $₹500$, respectively. Find the maximum profit (Write the answer excluding $₹$ symbol).

In order to supplement daily diet, a person wishes to take some $X$ and some $Y$ tablets. The contents of iron, calcium and vitamins in $X$ and $Y$ (in milligrams per tablet) are given as below:

The person needs at least $18$ milligrams of iron, $21$ milligrams of calcium and
$16$ milligram of vitamins. The price of each tablet of $X$ and $Y$ is Rs $2$ and
Re $1$ respectively. How many tablets of each should the person take in order to
satisfy the above requirement at the minimum cost?

A company makes $3$ model of calculators: $A, B$ and $C$ at factory $I$ and factory $II.$ The company has orders for at least $6400$ calculators of model $A, 4000$ calculator of model $B$ and $4800$ calculator of model $C.$ At factory $I, 50$ calculators of model $A, 50$ of model $B$ and $30$ of model $C$ are made every day; at factory $II, 40$ calculators of model $A, 20$ of model $B$ and $40$ of model $C$ are made everyday. It costs Rs $12000$ and Rs $15000$ each day to operate factory $I$ and $II,$ respectively. Find the number of days each factory should operate to minimise the operating costs and still meet the demand.






 

Maximise and Minimise $Z=3x – 4y$ subject to

$x-2y\le 0$

$-3x+y\le 4$

$x-y\le 6$

$x,y\ge 0$

Write the maximum value.