Initially, three firms a, b, and c share the market for a certain commodity. firm a has 30% of the market, firm b has 45%, and c has 25%. each year, the following changes occur:

• a keeps 75% of its customers, while losing 15% to b and 10% to c.
• b keeps 60% of its customers, while losing 5% to a and 35% to c.
• c keeps 65% of its customers, while losing 15% to a and 20% to b.

(a) what is the current market share vector (ordered for a, b, and c)?
(b) find the transition matrix for this scenario.
(c) find the share of the market that each company has after two years.

The production manager of rordan corporation has submitted the following quarterly production forecast for the upcoming fiscal year: 1st quarter 2nd quarter 3rd quarter 4th quarter units to be produced 10,800 8,500 7,100 11,200 each unit requires 0.25 direct labor-hours, and direct laborers are paid $20.00 per hour. required: 1. prepare the company’s direct labor budget for the upcoming fiscal year. assume that the direct labor workforce is adjusted each quarter to match the number of hours required to produce the forecasted number of units produced. 2. prepare the company’s direct labor budget for the upcoming fiscal year, assuming that the direct labor workforce is not adjusted each quarter. instead, assume that the company’s direct labor workforce consists of permanent employees who are guaranteed to be paid for at least 2,500 hours of work each quarter. if the number of required direct labor-hours is less than this number, the workers are paid for 2,500 hours anyway. any hours worked in excess of 2,500 hours in a quarter are paid at the rate of 1.5 times the normal hourly rate for direct labor.