Please help me get the answer ,all of my questions are in my attached files, thank you very much.

Project 2 Copy 3 Problem 1: Algebraically solve the following equations. The Method of Substitution of Variables should be helpful. You may not use Newton's Method. Your final answers should be accurate to 3 places after the decimal point. a. 5000e 6 R 2000e3 R 8000 2 5 4 ln x b. 3 ln x Problem 2: Wonder Company manufactures widgets. The Revenue Function is a quadratic function which has associated the following partial table of inputs (thousands of items produced) and outputs (millions of dollars earned): X (inputs) 10 20 30 Y (outputs) 70 150 120 a. Algebraically determine the formula for y in terms of x. Make sure that your answer is in standard form and identify the coefficients of the quadratic function. b. Algebraically determine the coordinates of the vertex of the graph of the function. Is this a maximum or minimum point? Explain. Now interpret your results. What is the optimum revenue and for what level of production does this occur? c. Algebraically determine what number of units must be produced to result in a revenue of 100. In this problem your final answers should be correct to 2 places after the decimal point. Problem 3: Betty and Bob are going to buy a statue from Art, the artist. They are offered 3 payments plans: a. $5000 paid now b. $2500 paid now and $3000 paid in 1 year c. $6000 paid in 18 months. If rates are 10% per annum effective then algebraically find the plan that is Best, Next, and Worst for Betty and Bob. Be sure to find the monetary difference and have your final answers correct to 2 places after the decimal point. Problem 4: Boris invests $10,000 now and $4,000 in 1 year. 2 years from now his account balance is $18,000. Bela invests $6,000 now and $3,600 in 6 months. 1 year from now his account balance is $12,000. Algebraically determine, using compound interest, who did better. Your final numerical answers which explain your response should be correct to 3 places after the decimal point. Problem 5: Betty and Bob are interested in borrowing money for 4 years as per compound interest. They have shopped around and have found the following plans: Plan 1: 8% per annum continuously compounded for the first year and 9% per annum continuously compounded for the next 3 years. Plans 2: 10% per annum continuously compounded for the first 18 months and 6% per annum compounded monthly for the remainder of the time. Plan 3: 9% per annum compounded semiannually for the first 9 months and 8% per annum compounded quarterly for the remainder of the time. Plan 4: 8% per compounding period of 8 months. This is to last for the entire 4 years. For each plan algebraically find the effective rate of interest per annum and the equivalent continuous rate of interest per annum. Rank the plans from Best to Worst for Betty and Bob. Your final numerical answers should be correct to 3 places after the decimal point. Problem 6: Day of the Quants, Problem 7 from Section 20. Problem 7: Betty and Bob have lost some data for an account that earns interest at a fixed continuous rate per annum, R. a. After 3 years and 6 months the account value is $5,600. After 8 years and 9 months the account value is $12,300. Algebraically find the rate R, and the initial investment, P. Your final answers should be correct to 3 places after the decimal point. b. Algebraically generalize your work. After T1 years the account value was A1 . After T2 years the account value was A2 . Find the continuous per annum rate, R, and the initial investment, P. Be sure to show all of your algebraic work. Take care to simplify the expression for P into a quotient with a nice power of A2 in the numerator and a nice power of A1 in the denominator. The powers (exponents) should only involve T1 and T2 . E should not appear. The section of your text on exponents and logarithms should be AW P 2 . helpful. A1V Problem 8a: Algebraically show that A Pe RT if and only if ln(A) versus T is linear. Find the slope, m, and the vertical intercept, d, in terms of P and R. 8b. Betty and Bob have an account that is growing approximately exponentially. The account value, A, versus the time, T, in years is given by the following table of partial inputs and outputs: T 2 3 5 7 8 A 6200 7000 11,500 16,400 19,000 Find the equation of the Least Squares Line of ln(A) versus T. Using part 8a algebraically predict A for T = 10. What is the approximate rate of return, R, and the principal, P? Your final numerical answers should be accurate to 3 places after the decimal point. Problem 9: Betty and Bob seek treasure and adventure at a dessert oasis. Each unit of (gold, jewels, coins) is Worth ($2 million, $3 million, $2 million) and Takes (1 hour, 2hours, 2 hours) to find and Weighs (2 pounds, 1 pound, 2 pounds) and Occupies (2 units, 1 unit, 1 unit) of space. If they have at most 14 hours to seek, can carry at most 20 pounds, and have at most 16 units of space then find the number of units of gold, jewels, and coins that would maximize the value of the treasure. What is this maximum value? Use the Simplex Method as detailed in the appendix Linear Programming & the Simplex Method. Be sure to show all your tableau work