Quantitative Methods Answers

A manufacturing concern manufactures two products A and B. The products go through three processes: processing, fabrication and assembly. The manufacturing time per unit required to make them, the profit per unit, and the capacity available at each work center are as follows :

WORK CENTER (IN HOURS)

product Machining frabication assembly profit per unit

A 1 5 3 80

B 2 4 1 100

total capacity 720 1800 900

A) Formulate the above information to optimize the profit of the manufacturing concern

B) Find graphical solution.

Based on below data, test that Brand preference and Education qualifications are independent, at 5% level of significance.

(No. OF PERSONS PREFERRING BRANDS)

Education Brand A Brand B Brand C

qualification

SSC 22 34 35

HSC 28 35 28

Graduate 30 44 27

Post graduate 55 42 28

Assume that the test scores from a college admissions test are normally distributed, with a

mean of 450 and a standard deviation of 100.

a. What percentage of the people taking the test score between 400 and 500?

b. Suppose someone receives a score of 630. What percentage of the people taking the

test score better? What percentage score worse?

c. If a particular university will not admit anyone scoring below 480, what percentage of

the persons taking the test would be acceptable to the university?

The mean fat content of a brand of butter is 20.0 mgs. A new process is proposed to lower the fat content without affecting the flavour. To test the new process16 packets of butter are taken at random and the sample mean fat content is found to be 18.5 mgs with a standard deviation of 2 mgs. Test 5 % level of significance is the new process justified.

Use Runge-Kutta method of order 2 to solve y′ = xy, y(1) = 1, in [1, 1.4] by taking step-length h = 0.2

Use modified Euler’s method with one step to find the value of y at x = 0.1 to five significant figures, where dy/dx = x^2+y, y=0.94, when x = 0.

Given that y' = x+y^2, y(0)=1, find y(0.2), using the backward Euler’s method.

Solve y′ = x−y^2, y(0) = 1 using the forward Euler method for in [0, 0.6] by taking h = 0.2.

Given dy/dx = y-x,where y(0) = 2, find y(0.1) and y(0.2) by Euler’s method up to two decimal places.

A slider in a machine moves along a fixed straight rod. Its distance x(in cm) along the rod is given at various times t (in secs).

T : 0 0.1 0.2 0.3 0.4 0.5 0.6

x : 30.28 31.43 32.98 33.54 33.97. 33.48 32.13

Evaluate dx/dt at t = 0.1 And. at t = 0.5