Graphical Method of Solving Linear Programming Problems

Q.

You work as a sales representative. You earn $\$400$ per week plus $5\%$ of your total sales for the week.

Part A: Last week, you had total sales of $\$5000$. Find your total earnings. Show your work.

Part B: One week, you earned $\$1350$. Let s represent your total sales that week. Write an equation that you can use to find s.

Part C: Using your equation from Part B, find s. Show all steps clearly.

Q. A manufacturing company makes two types of television sets; one is black and white and the other is colour. The company has resources to make at most 350 sets a week. It takes Rs 1800 to make a black and white set and Rs 2700 to make a coloured set. The company can spend not more than Rs 648000 a week to make television sets. If it makes a profit of Rs 500 per black and white set and Rs 600 per coloured set. Formulate this problem as an LPP given that the objective is to maximise the profit. what is the maximum profit ?

1. 177000
2. 175000
3. 188000
4. 144000

Q. Solve.
X employed Y. The terms of service agreement are
(a) The employee has to serve the organisation for 5 years.
(b) The employee shall not accept any other similar engagement during the term of agreement.
(c) The employee shall not accept similar engagement after the termination of services.
(d) The employee shall not compete with his employer after the termination of services.
State the legal position of the terms of service agreement.

Q. Draw the graph of linear equations $y=x$ and $y=x+1$ on the same Cartesian plane. What do you observe?

Q. By increasing the list price of a book by ₹12, a person can buy 24 books less for ₹1728. The original price of the book was_____.

1. ₹16
2. ₹24
3. ₹18
4. ₹20

Q. By increasing the list price of a book by ₹12, a person can buy 24 books less for ₹1728. The original price of the book was_____.

1. ₹24
2. ₹16
3. ₹20
4. ₹18

Q.

A company manufactures cassettes and its cost equation for a week is $C=300+1.5x$ and its revenue equation is $R=2x$, where $x$ is the number of cassettes sold in a week. How many cassettes must be sold for the company to realize a profit?

Q.

The cost of manufacturing$x$ telephones by TATA is given by $C=3000+200x,$ and the revenue from selling these is $R=300x$. How many telephone must be produced in order to realize a profit.

Q.

At compound interest rate if a certain sum of money doubles in n years then the amount will be four-fold in ______.

1. $4n$ years

2. $2n$ years

3. $2n^2$ years

4. $n^2$ years

Q. P and Q are two food packets. Each packet (containing 30 g) of food P contains 12 units of calcium, 4 units of iron, 8 units of cholesterol and 6 units of vitamin A. Each packet of the same quantity of food Q contains 3 units of calcium, 20 units of iron, 4 units of cholesterol and 3 units of vitamin A. The diet requires at least 240 units of calcium, at least 460 units of iron and at most 300 units of cholesterol. What is the minimum amount of vitamin A?

1. 150
2. 200
3. 100
4. 175

Q. Raj was given a linear programming problem to solve in an interview. The constraints of the problems are x ≥ 0, y ≥ 0, 3x+5y ≤ 15, 5x+2y ≤ 10. The interviewer told him one of the four points given below is the optimal solution for the problem and theorem 1 in linear programming would help him to find the answer. Which of the following points is the optimal solution?

1. $(\frac{20}{17},\frac{45}{17})$

2. $(\frac{20}{19},\frac{41}{17})$

3. $(\frac{20}{19},\frac{45}{19})$

4. $(\frac{20}{19},\frac{41}{19})$