Amit M Agarwal Solutions for Chapter: Linear Programming, Exercise 2: Target Exercises

A firm has to transport $1200$ packages using large vans which can carry $200$ packages each and small vans which can take $80$ packages each. The cost for engaging each large van is $₹400$ and each small van is $₹200$. Not more than $₹3000$ is to be spent on the job and the number of large vans cannot exceed the number of small vans. Then, the minimum cost for the firm is

A manufacturer has three machines $\mathrm{I}, \mathrm{II}$ and $\mathrm{III}$ installed in his factory. Machines $\mathrm{I}$ and $\mathrm{II}$ are capable of being operated for utmost $12$ hours  whereas, machine $\mathrm{III}$ must be operated for at least $5$ hours a day. She produces only two items $M$ and $N$ each requiring the use of all the three machines.

The number of hours required for producing $\mathrm{I}$ unit of each of $M$ and $N$ on the three machines are given in the following table:

She makes a profit of $₹600$ and $₹400$ on items $M$ and $N$, respectively,

Then, to maximise the profit, number of units of item $M$, the manufacturer has to produce, is

Anil wants to invest utmost $₹12000$ is bonds $A$ and $B$. According to the rules, he has to invest at least $₹2000$ in bond $A$ and at least $₹4000$ in bond $B$. If the rate of interest in bond $A$ is $8\%$ per annum and in bond $B$ is $10\%$ per annum, then to maximise the interest, the investment in bond $A$ and $B$ are respectively

The maximum value of $Z$, where $Z=4x+2y$ subject to constraints $4x+2y\ge 46,x+3y\le 24$ and $x,y\ge 0$ is

If the given constraints are $5x+4y\ge 2, x\le 6$ and $y\le 7$, then the maximum value of the function $Z=x+2y$ is

The minimum value of the objective function $Z=2x+10y$ subject to constraints $x\ge 0, y\ge 0$ $x-y\ge 0, x-5y\le -5$ is

Reshma wishes to mix two types of food $P$ and $Q$ in such a way that the vitamin contents of the mixture contain at least $8 \mathrm{units}$ of vitamin $A$ and $11 \mathrm{units}$  of vitamin $B$. Food $P$ costs $₹60/\mathrm{kg}$ and food $Q$  costs $₹80/\mathrm{kg}$. Food $P$ contains $3 \mathrm{units}/\mathrm{kg}$  of vitamin $A$ and $5 \mathrm{units}/\mathrm{kg}$ of vitamin $B$, while food $Q$ contains $4 \mathrm{units}/\mathrm{kg}$ of vitamin $A$ and $2 \mathrm{units}/\mathrm{kg}$ of vitamin $B$. Then, the minimum cost of the mixture is

The linear programming problem Maximise $Z=x_1+x_2$ subject to constraints are $x_1+2x_2\le 2000, x_1+x_2\le 1500, x_2\le 600$,

$x_1\ge 0$ and $x_2\ge 0$ has