Afirms production is represented by the following cobb-douglas function: = 2 1 3 2 3. the rental rate, r, of capital is given by $200 and the price of labor is $100. a. for a given level of output, what should be the ratio of capital to labor in order to minimize costs? b. how much capital and labor should be used to produce those 200 units? c. what is the minimum cost of producing 200 units? d. what is the minimum cost of producing 350 units? e. does this production function exhibit increasing, decreasing, or constant returns to scale? answer based on the cost calculations in parts c and d.

Instructions: use the following information to construct the 2000 balance sheet and income statement for carolina business machines. round all numbers to the nearest whole dollar. all numbers are in thousands of dollars. be sure to read the whole problem before you jump in and get started. at the end of 1999 the firm had $43,000 in gross fixed assets. in 2000 they purchased an additional $14,000 of fixed asset equipment. accumulated depreciation at the end of 1999 was $21,000. the depreciation expense in 2000 is $4,620. at the end of 2000 the firm had $3,000 in cash and $3,000 in accounts payable. in 2000 the firm extended a total of $9,000 in credit to a number of their customers in the form of accounts receivable. the firm generated $60,000 in sales revenue in 2000. their cost of goods sold was 60 percent of sales. they also incurred salaries and wages expense of $10,000. to date the firm has $1,000 in accrued salaries and wages. they borrowed $10,000 from their local bank to finance the $15,000 in inventory they now have on hand. the firm also has $7,120 invested in marketable securities. the firm currently has $20,000 in long-term debt outstanding and paid $2,000 in interest on their outstanding debt. over the firm's life, shareholders have put up $30,000. eighty percent of the shareholder's funds are in the form of retained earnings. the par value per share of carolina business machines stock is

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This exercise illustrates that poor quality can affect schedules and costs. a manufacturing process has 130 customer orders to fill. each order requires one component part that is purchased from a supplier. however, typically, 3% of the components are identified as defective, and the components can be assumed to be independent. (a) if the manufacturer stocks 130 components, what is the probability that the 130 orders can be filled without reordering components? (b) if the manufacturer stocks 132 components, what is the probability that the 130 orders can be filled without reordering components? (c) if the manufacturer stocks 135 components, what is the probability that the 130 orders can be filled without reordering components?