A manager must decide which type of machine to buy, A, B, or C. Machine costs (per individual machine) are as follows: Machine Cost
A $80,000
B $70,000
C $40,000

Product forecasts and processing times on the machines are as follows:

PROCCESSING TIME PER UNIT (minutes)
Product Annual Demand A B C
1 24,000 1 4 6
2 8,000 1 3 5
3 30,000 6 4 3
4 18,000 6 5 1

Required:
a. Assume that only purchasing costs are being considered. Compute the total processing time required for each machine type to meet demand, how many of each machine type would be needed, and the resulting total purchasing cost for each machine type. The machines will operate 10 hours a day, 240 days a year.
b. Compute total purchasing costs using these rounded machine quantities. Enter the resulting total purchasing cost as a whole number.)

Suppose a firm faces a fixed price of output, 푝푝= 1200. the firm hires workers from a union at a daily wage, 푤푤, to produce output according to the production function 푞푞= 2퐸퐸12. there are 225 workers in the union. any union worker who does not work for this firm is guaranteed to find nonunion employment at a wage of $96 per day. a. what is the firm’s labor demand function? b. if the firm is allowed to choose 푤푤, but then the union decides how many workers to provide (up to 225) at that wage, what wage will the firm set? how many workers will the union provide? what is the firm’s output and profit? what is the total income of the 225 union workers? c. now suppose that the union sets the wage, but the firm decides how many workers to hire at that wage (up to 225). what wage will the union set to maximize the total income of all 225 workers? how many workers will the firm hire? what is the firm’s output and profit? what is the total income of the 225 union workers? [hint: to maximize total income of union, take the first order condition with respect to w and set equal to 0.]