Determine the maximum value of $Z=11 x+7 y$ subject to the constraints $2 x+y \leq 6, x \leq 2, x \geq 0, y \geq 0$.

Maximise $Z=3 x+4 y$, subject to the constraints $x+y \leq 1, x \geq 0, y \geq 0$.

Maximise the function $Z=11 x+7 y$, subject to the constraints $x \leq 3$, $y \leq 2, x \geq 0$ and $y \geq 0$.

Minimise $Z=13 x-15 y$ subject to the constraints $x+y \leq 7$, $2 x-3 y+6 \geq 0, x \geq 0$ and $y \geq 0$.

Determine the maximum value of $Z=3 x+4 y$, if the feasible region (shaded) for a LPP is shown in following figure.

Feasible region (shaded) for a LPP is shown in following figure. Maximise $Z=5 x+7 y$.

The feasible region for a LPP is shown in following figure. Find the minimum value of $Z=11 x+7 y$.

The feasible region for a LPP is shown in following figure. Find the maximum value of Z.

The feasible region for a LPP is shown in the following figure. Evaluate $Z=4 x+y$ at each of the corner points of this region. Find the minimum value of $Z$, if it exists.

In following figure, the feasible region (shaded) for a LPP is shown. Determine the maximum and minimum value of $Z=x+2 y$.

A manufacturer of electronic circuits 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 ₹ 50 and that on type $B$ circuit is ₹ 60 , formulate this problem as a LPP, so that the manufacturer can maximise his profit.

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. Formulate this problem as a LPP given that the objective is to minimise cost.

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 min on the threading machine and 3 $\min$ on the slotting machine. A box of type $B$ screws requires 8 min on the threading machine and 2 min on the slotting machine. In a week, each machine is available for 60 h . On selling these screws, the company gets a profit of ₹ 100 per box on type $A$ screws and ₹ 170 per box on type $B$ screws. Formulate this problem as a LPP given that the objective is to maximise profit.

A company manufactures two types of sweaters type $A$ and type $B$. It costs ₹ 360 to make a type $A$ sweater and ₹ $120$ to make a type $B$ sweater. The company can make atmost 300 sweaters and spend atmost ₹ $72000$ 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 ₹ 200 for each sweater of type A and ₹ 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 $50 \mathrm{~km} / \mathrm{h}$. He has to spend ₹ 2 per km on petrol. If he rides it at a faster speed of $80 \mathrm{~km} / \mathrm{h}$, the petrol cost increases to ₹ 3 per km. He has atmost ₹ 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.

Refer to question 11. How many of circuits of type $A$ and of type $B$, should be produced by the manufacturer, so as to maximise his profit? Determine the maximum profit.

Refer to question 12 . What will be the minimum cost?

Refer to question 13 . Solve the linear programming problem and determine the maximum profit to the manufacturer.

Refer to question 14 . How many sweaters of each type should the company make in a day to get a maximum profit? What is the maximum profit?

Refer to question 15. Determine the maximum distance that the man can travel.

Maximise $Z=x+y$ subject to $x+4 y \leq 8,2 x+3 y \leq 12,3 x+y \leq 9$, $x \geq 0$ and $y \geq 0$.

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 ₹ 80000 per week. Profits per unit for models $X$ and $Y$ are ₹ $1000$ and ₹ 500 , respectively. How many bikes of each model should the manufacturer produce, so as to yield a maximum profit? Find the maximum profit.

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

The person needs atleast 18 mg of iron, 21 mg of calcium and 16 mg of vitamins. The price of each tablet of $X$ and $Y$ is ₹ $2$ and ₹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 atleast 6400 calculators of model $A, 4000$ calculators of model $B$ and 4800 calculators of model $C$. At factory I, 50 calculators of model $A, 50$ of model $B$ and 30 of model $C$ are made everyday; at factory II, 40 calculators of model $A, 20$ of model $B$ and 40 of model $C$ are made everyday. It costs ₹ 12000 and ₹ 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 $Z=3 x-4 y$ subject to $x-2 y \leq 0,-3 x+y \leq 4$, $x-y \leq 6$ and $x, y \geq 0$.

The corner points of the feasible region determined by the system of linear constraints are $(0,0),(0,40),(20,40),(60,20),(60,0)$. The objective function is $Z=4 x+3 y$. Compare the quantity in column $A$ and column $B$.

The feasible solution for a LPP is shown in following figure. Let $Z=3 x-4 y$ be the objective function. Minimum of $Z$ occurs at

Refer to question 27. Maximum of $Z$ occurs at

Refer to question 7, maximum value of $Z+$ minimum value of $Z$ is equal to

The feasible region for an LPP is shown in the following figure. Let $F=3 x-4 y$ be the objective function. Maximum value of $F$ is

Minimum value of F is

Corner points of the feasible region for an LPP are $(0,2),(3,0),(6,0)$, $(6,8)$ and $(0,5)$. Let $F=4 x+6 y$ be the objective function. The minimum value of $F$ occurs at

Maximum of F $-$ minimum of F is equal to

Corner points of the feasible region determined by the system of linear constraints are $(0,3),(1,1)$ and $(3,0)$. Let $Z=p x+q y$, where $p, q>0$. Condition on $p$ and $q$, so that the minimum of $Z$ occurs at $(3,0)$ and $(1,1)$ is

In a LPP, the linear inequalities or restrictions on the variables are called ....... .

In a LPP, the objective function is always... .

In the feasible region for a LPP is ......, then the optimal value of the objective function $Z=a x+b y$ may or may not exist.

In a LPP, if the objective function $Z=a x+b y$ has the same maximum value on two corner points of the feasible region, then every point on the line segment joining these two points give the same ........ value.

A feasible region of a system of linear inequalities is said to be ......., if it can be enclosed within a circle.

A corner point of a feasible region is a point in the region which is the ....... of two boundary lines.

The feasible region for an LPP is always a ....... polygon.

If the feasible region for a LPP is unbounded, maximum or minimum of the objective function $Z=a x+b y$ may or may not exist.

Maximum value of the objective function $Z=a x+b y$ in a LPP always occurs at only one corner point of the feasible region.

In a LPP, the minimum value of the objective function $Z=a x+b y$ is always 0 , if origin is one of the corner point of the feasible region.

In a LPP, the maximum value of the objective function $Z=a x+b y$ is always finite.