A farmer is producing Grains and Vegetables with a given set of input mix and water. The input mix includes fertilizer and labor in fixed ratios so they can be treated as one variable, with grains needing 5 units of input and and vegetables needing 50 units of input per acre. Water is also used, grains need 4 units of water and vegetables need 8 units of water per acre. The farmer only has 1,245 units of the input mix and 300 units of water. The profit per acre is $5 for grains and $25 for vegetables. The farmer wants to maximize profits and there is no acreage constraint. (a) Formulate a linear programming model algebraically

Outstanding stock consists of 8,300 shares of cumulative 7% preferred stock with a $10 par value and 4,300 shares of common stock with a $1 par value. during the first three years of operation, the corporation declared and paid the following total cash dividends. year dividend declared 2016 $ 0 2017 $ 7,300 2018 $ 45,000 the amount of dividends paid to preferred and common shareholders in 2018 is:

The monthly payment m of a loan of amount p for y years with an interest rate r can be calculated by the formula: m = p(r/12) 1 â’ (1 + r/12)â’12y calculate the monthly payment and the cummulative total payment for a $100,000 loan with an interest rate of 4.85% if taken out for 10 years, for 11 years, etc., up to a 30 year term. display the results in a three-column table where the first column is the number of years, the second is the monthly payment, and the third is the cummulative total payment. note: use format bank; for this problem. also, remember to represent the interest rate as a decimal (e.g. 0.0485) 2. a torus-shaped water tube is designed to have a volume of 8, 000in3 . the volume of the tube, v , and its surface area, s, are given by: v = 1 4 ď€ 2 (a + b)(b â’ a) 2 s = ď€ 2 (b 2 â’ a 2 ) if a = kb, determine s, a, and b for k = 0.2, 0.3, 0.7. display the results in a table

Net income and owner's equity for four businesses four different proprietorships, jupiter, mars, saturn, and venus, show the same balance sheet data at the beginning and end of a year. these data, exclusive of the amount of owner's equity, are summarized as follows: total assets total liabilities beginning of the year $550,000 $215,000 end of the year 844,000 320,000 on the basis of the preceding data and the following additional information for the year, determine the net income (or loss) of each company for the year. (hint: first determine the amount of increase or decrease in owner's equity during the year.) jupiter: the owner had made no additional investments in the business and had made no withdrawals from the business. mars: the owner had made no additional investments in the business but had withdrawn $36,000. saturn: the owner had made an additional investment of $60,000 but had made no withdrawals. venus: the owner had made an additional investment of $60,000 and had withdrawn $36,000. jupiter net income $ mars net income $ saturn net income $ venus net income $