Help with this business mathematics. Please show the calculation
1. A sales man has the following record of sales during three months for three items A, B and C which have different rates of commission.
Month Sales in units Total Commission ($)
A B C
May 90 100 20 800
June 130 50 40 900
July 60 100 30 850
Using the matrix method, find out the rates of commission on items A, B and C. (4 points)
2. One half of a country’s population lives in the city and one half in the suburbs. There is an 80% chance that a suburban resident will remain in the suburbs and a 20% chance that he or she will move to the city within the next month. A city dweller has a 60% chance of staying in the city and 40% moving to the suburbs. Determine:
a) The percentage of the population in the suburb and the city one and two months from now.
b) The steady state probabilities. (4 points)
3. An economy consists of three industries R, S and T. The interrelationships between the productions of these industries are as shown below. Units in “000” tonnes.
R S T Consumer Total
R 50 20 40 70 180
S 20 30 20 90 160
T 30 20 20 50 120
Required:
a) Determine the Leontief inverse matrix. (6 points)
b) If the demand is expected to change for R, S and T and it becomes 60, 110 and 60 respectively, what must the total output be for each industry to satisfy this demand? (4points)
