a) A firm can produce 3 types of cloths say A , B and C. Three kinds of wool were required for it, say red wool , green wool and blue wool. One unit length of type A cloth needs 2 yards of red wool and 3 yards of blue wool. One unit length of type B cloth needs 3 yards of red wool , 2 yards of green wool and 2 yards of blue wool, and one unit length of type C cloth needs 5 yards of green wool and 4 yards of blue wool. The firm has only a stock of 8 yards of red wool,10 yards of green wool and 15 yards of blue wool. It is assumed that the income obtained from one unit length of type A cloth is Ksh.300 of type B cloth is Ksh.500 and of type C cloth is Kshs.400 .Formulate mathematical model to the problem and solve the problem
b) Maximize 100𝑥1+600𝑥2
Subject to 2𝑥1+𝑥2+𝑥3=300 3𝑥1+4𝑥2+𝑥4=509 4𝑥1+7𝑥2+𝑥5=812 𝑥1,𝑥2,𝑥3,𝑥4,𝑥5≥0
c) A firm manufacturer has 3 products A , B ,C .The profit from A,B,C are Rs.6,Rs.4,Rs.8 resp. A firm has two machines and given below is required processing time in minutes for each machines on each product.
d) The products A,B and C are produced in three machine centres X,Y and Z. Each product involves operation of each of the machine centres. The time required for each operation for unit amount of each product is given below. 100, 77 and 80 hours are available at machine centres X,Y and Z respectively. The profit per unit of A, B and C is 12000,3000 and 1000 shillings respectively. Find a suitable product mix so as to maximize the profit.
e) Draw the network for the project whose activities and their precedence relationship are as given below
f) Find an initial solution to the following transportation problem.
i) Use the northwest-corner method. (3 marks)
ii) Use the intuitive lowest-cost approach. (3 marks)
iii) What is the total cost of each method? (1 mark)