QUESTION 1

A restaurant has an annual demand for 914 bottles of California wine. It costs $2 to store 1 bottle for 1 year, and it costs $8 to place a reorder. (a) Find the optimum number of bottles per order. (b) How many times a year should the wine be ordered? (a) The optimum number of bottles per order is (Type a whole number.) (b) The wine should be ordered D times a year. (Round to one decimal place as needed.) Find the interest rate required for an investment of $5000 to grow to $6500 in 10 years if interest is compounded as follows. a. Annually b. Quarterly a. Write an equation which relates the investment of $5000, the desired value of $6500, and the time period of 10 years in terms of r, the yearly interest rate {written as a decimal), and m, the number of compounding periods per yeaL D The required annual interest rate if interest is compounded annually is %. (Round to two decimal places as needed.) b. The required annual interest rate if interest is compounded quarteriy is %. (Round to two decimal places as needed.) Find all the local maxima, local minima, and saddle points of the given function. f(x,y) = 2x2 + 3xy + 4y2 - 2x +10y Select the correct choice below and ll in any answer boxes within your choice. '3' A- There are local maxima located at (Simplify your answers. Type ordered pairs. Use a comma to separate answers as needed.) Q B. There are no local maxima. Select the correct choice below and ll in any answer boxes within your choice. '3' A- There are local minima located at (Simplify your answers. Type ordered pairs. Use a comma to separate answers as needed.) [:2- B. There are no local minima. Select the correct choice below and ll in any answer boxes within your choice. [:3' A- There are saddle points located at (Simplify your answers. Type ordered pairs. Use a comma to separate answers as needed.) (:5 B. There are no saddle points. The sales of a small company were $53,000 in its fourth year of operation and $77,000 in its sixth year. Let y represent sales in the xth year of operation. Assume that the data can be approximated by a straight line. (a) Find the slope of the sales line, and give an equation for the line in the form y = mx + b. (b) Use your answer from part (b) to nd out how many years must pass before the sales surpass $110,000. (a) The slope is D and the equation is y = D): + E. (Type integers or decimals.) (b) The sales will surpass $110,000 in years. (Round up to the nearest year.) For the function f(x,y) = 4)' 3y2 -I- x2 , nd f(3, - 2), f( - 5,3), f( - 4, - 5), and f(0,6). f(3, - 2) = (Type an exact answer, using radicals as needed.) f( - 5,3) = (Type an exact answer, using radicals as needed.) f( - 4, - 5) = (Type an exact answer, using radicals as needed.) f(0,6) = (Type an exact answer, using radicals as needed.)