Quantitative Methods Answers

1)                 Find the Lagrange’s interpolating polynomial of f(x) from the table of values given below and show that it is the same as the Newton’s divided differences interpolating polynomial.

A company has decided to produce a new cereal called ‘Nuts and Bran’ which contains only nuts (N) and bran (B). The company has RM15000 to spend on nuts and bran. The cost of nuts is RM1200 and RM800 for bran.

     a.   Draw an isocost curve showing the different combinations of nuts and bran that the company can purchase.

(10 marks)

    b.   What will hapeen to the original isocost line if:

1.     the capital reduce by 25%?
2.     the price of nuts increase by RM200?
3.     the price for both nuts and bran reduce by 15%?

Two neighbouring farmers, Farmer A and Farmer B,have to flood their fields on the same day. Each use one lock in the conservancy dam to supply his field with water. The lock at Farmer B field, however, has a faster flow rate than that at Farmer A’s. In addition, Farmer B opened his lock 30 minutes later than Farmer A did his. 

Question: When would the two fields have been supplied with the same volume of water?

To solve this problem, you need to use matrix methods.

Determine whether the coefficient matrix is well conditioned or not.

You need to also advise on the bound on the relative error of your solution.

What assumptions, if any, you had to make?

1. A company in the wholesale trade selling sportswear and stocks two brands, A and B, of football kit, each consisting of a shirt, a pair of shorts and a pair of socks. The costs for brand A are Sh.50 for a shirt, Sh30 for a pair of shorts and Sh10 for a pair of socks and those for brand B are Sh.60.25 for a shirt, Sh.40 for a pair of shorts and Sh.10 for a pair of socks. Three customers X, Y, Z demand the following combinations of brands; X, 36 kits of brand A and 48 kits of brand B Y, 24 kits of brand A and 72 kits of brand B Z, 60 kits of brand

A Required:

i) Express the costs of brands A and B in matrix form, then the demands of the customers, X,Y and Z in matrix form. (5 marks)

ii) By forming the product of the two matrices that you obtain in the previous part, deduce the detailed costs to each of the customers. (5 marks)