Biwei’s Barbershop is a business in a perfectly competitive market with total cost of TC = 0.5Q 2 per day. The corresponding marginal cost is MC=Q. Assume that the market price of a haircut is $15.

How many haircuts should Biwei give each day if he wants to maximize his profit? What is the profit?

Afinancial institution, the thriftem bank, is in the process of formulating its loan policy for the next quarter. a total of $12 million is allocated for that purpose. being a full-service facility, the bank is obligated to grant loans to different clientele. the following table provides the types of loans, the interest rate charged by the bank, and the possibility of bad debt as estimated from past experience.type of loaninterest rateprobability of bad debtpersonal.140.10car.130.07home.120.03farm.125.05commercial.100.02 bad debts are assumed unrecoverable and hence produce no interest revenue either. competition with other financial institutions in the area requires that the bank allocate at least 40% of the total funds to farm and commercial loans. to assist the housing industry in the region, home loans must equal at least 50% of the personal, car, and home loans. the bank also has a stated policy specifying that the overall ratio for bad debts on all loans may not exceed .04. formulate this problem as a linear program. define your variables clearly and write all the constraints explaining the significance of each.

Pettijohn inc. the balance sheet and income statement shown below are for pettijohn inc. note that the firm has no amortization charges, it does not lease any assets, none of its debt must be retired during the next 5 years, and the notes payable will be rolled over. balance sheet (millions of $) assets 2016 cash and securities $ 1,554.0 accounts receivable 9,660.0 inventories 13,440.0 total current assets $24,654.0 net plant and equipment 17,346.0 total assets $42,000.0 liabilities and equity accounts payable $ 7,980.0 notes payable 5,880.0 accruals 4,620.0 total current liabilities $18,480.0 long-term bonds 10,920.0 total debt $29,400.0 common stock 3,360.0 retained earnings 9,240.0 total common equity $12,600.0 total liabilities and equity $42,000.0 income statement (millions of $) 2016 net sales $58,800.0 operating costs except depr'n $54,978.0 depreciation $ 1,029.0 earnings bef int and taxes (ebit) $ 2,793.0 less interest 1,050.0 earnings before taxes (ebt) $ 1,743.0 taxes $ 610.1 net income $ 1,133.0 other data: shares outstanding (millions) 175.00 common dividends $ 509.83 int rate on notes payable 1. what is the firm's current ratio? (points : 6) 0.97 1.08 1.20 1.33 2. what is the firm's quick ratio? (points : 6) 0.49 0.61 0.73 0.87 3. what is the firm's total assets turnover? (points : 6) 0.90 1.12 1.40 1.68 4. what is the firm's inventory turnover ratio? (points : 6) 4.38 4.59 4.82 5.06 5. what is the firm's debt ratio? (points : 6) 45.93% 51.03% 56.70% 70.00% 6. what is the firm's roa? (points : 6) 2.70% 2.97% 3.26% 3.59% 7. what is the firm's roe? (points : 6) 8.54% 8.99% 9.44% 9.91%

In the fall, jay thompson decided to live in a university dormitory. he signed a dorm contract under which he was obligated to pay the room rent for the full college year. one clause stated that if he moved out during the year, he could sell his dorm contract to another student who would move into the dormitory as his replacement. the dorm cost was $5000 for the two semesters, which jay had already paid a month after he moved into the dorm, he decided he would prefer to live in an apartment. that week, after some searching for a replacement to fulfill his dorm contract, jay had two offers. one student offered to move in immediately and to pay jay $300 per month for the eight remaining months of the school year. a second student offered to move in the second semester and pay $2500 to jay. jay estimates his food cost per month is $500 if he lives in the dorm and $450 if he lives in an apartment with three other students. his share of the apartment rent and utilities will be $404 per month. assume each semester is 4.5 months long. disregard the small differences in the timing of the disbursements or receipts. what is the cost of the cheapest alternative?