Quantitative Methods Answers

The buyer for Payless Shoe store decided to order a woman’s shoe at a buyers’ meeting in Miami. The shoe  will be part of the company’s Christmas promotion. New designs are coming out after Christmas, so the shoes have to be sold during the Christmas season. Payless plans to hold a special December clearance sale, in an attempt to sell all shoes not sold  by November 31st. The shoes will retail at $50 per pair and the company makes a profit of $15 on each pair. At the sale price of $21 per pair, all surplus shoes can be expected to sell during the December sale. The expected demand for the shoes is 700 pairs with a standard deviation of 300 pairs. How many pairs of the shoe should the buyer order?

Consider the function f(x) = 3x + sin(x) − e x . (1.1) Use the bisection method to determine a root of f(x) in the interval (0.0, 0.5), using up to ten iterations.

Use newton raphson method to Find an approximate root of x3

-5x+3 = 0 that lies in

[0,1]. Find the approximation to three decimal places.

Use Euler and modified Euler method with one step find the value of y at x=0.1 for given dy/dx=x^2 +y and y=0.94 when x=0

Question 2: Discrete Random Variable

The BRIT Sports Bar sells a large quantity of Guinness every Saturday. From past records, the pub has determined the following probabilities for sales:

Number of Crates (X) 

P(x)

18-0.15

19-0.10

20-0.32

21-0.05

22-0.13

23-0.25

a. Verify that this [P(x)] is a probability distribution. ​(2 marks)

b. Find the probability that the number of crates sold will be at least 22.  (3 marks)

c. Find the probability that the number of crates sold will be at most 20.  (3 marks)

d. What is the expected value for the number of crates sold for any given Saturday? 

(4 marks)

e. Calculate the variance of the distribution? ​(6 marks)

f. Determine the standard deviation of the distribution? ​(2 marks)

can workout be shown please.

find the root between (2,3) of x^3-2x-5=0, by using false position method

Q4. Convert the following linear programming problem into dual

problem.

Maximise

Z = 22x1 + 25x2 +19x3

Subject to:

18x1 + 26x2 + 22x3 ≤ 350

14x1 + 18x2 + 20x3 ≥180

17x1 + 19x2 + 18x3 = 205

x1, x2, x3 ≥ 0

A firm manufactures two products; the net profit on product 1 is Birr 3 per unit and Birr 5 per unit on product 2. The manufacturing process is such that each product has to be processed in two departments D1 and D2. Each unit of product1 requires processing for 1 minute at D1 and 3 minutes at D2; each unit of product 2 requires processing for 2 minutes at D1 and 2 minutes at D2. Machine time available per day is 860 minutes at D1 and 1200 minutes at D2. How much of product 1 and 2 should be produced every day so that total profit is maximum. (solve with graphical method)