The grading of roadways requires both labor and machine time. Assume that from empirical experience, the number of miles of roadway H that can be graded as a function of L hours of labor and M hours of machine time is given by: H = 0.6L0.25 M0.6 Labor costs $70/hr, machine time costs $400/hr, and 24 miles of road must be graded. a) State this problem in terms of an objective function and constraint(s). b) Solve this problem by hand using the Lagrange multiplier method. Find the optimal values of L, M, and the Lagrange multiplier. c) Check your answer by enumeration using a programming language (Python) and by using Excel Solver. d) At the last minute, before your total cost estimate must be delivered, y

Identify which of the twelve basic functions listed below fit the description given.

Annuity payments are assumed to come at the end of each payment period (termed an ordinary annuity). however, an exception occurs when the annuity payments come at the beginning of each period (termed an annuity due). what is the future value of a 13-year annuity of $2,800 per period where payments come at the beginning of each period? the interest rate is 9 percent. use appendix c for an approximate answer, but calculate your final answer using the formula and financial calculator methods. to find the future value of an annuity due when using the appendix tables, add 1 to n and subtract 1 from the tabular value. for example, to find the future value of a $100 payment at the beginning of each period for five periods at 10 percent, go to appendix c for n = 6 and i = 10 percent. look up the value of 7.716 and subtract 1 from it for an answer of 6.716 or $671.60 ($100 × 6.716)

Wilson company paid $5,000 for a 4-month insurance premium in advance on november 1, with coverage beginning on that date. the balance in the prepaid insurance account before adjustment at the end of the year is $5,000, and no adjustments had been made previously. the adjusting entry required on december 31 is: (a) debit cash. $5,000: credit prepaid insurance. $5,000. (b) debit prepaid insurance. $2,500: credit insurance expense. $2500. (c) debit prepaid insurance. $1250: credit insurance expense. $1250. (d) debit insurance expense. $1250: credit prepaid insurance. $1250. (e) debit insurance expense. $2500: credit prepaid insurance. $2500.