a. Identify the feasible solution. b. Obtain the optimal solution.
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a. Identify the feasible solution.
b. Obtain the optimal solution.
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- A company manufacturers a product in the United States and sells it in England. The unit cost of manufacturing is 50. The current exchange rate (dollars per pound) is 1.221. The demand function, which indicates how many units the company can sell in England as a function of price (in pounds) is of the power type, with constant 27556759 and exponent 2.4. a. Develop a model for the companys profit (in dollars) as a function of the price it charges (in pounds). Then use a data table to find the profit-maximizing price to the nearest pound. b. If the exchange rate varies from its current value, does the profit-maximizing price increase or decrease? Does the maximum profit increase or decrease?You want to take out a 450,000 loan on a 20-year mortgage with end-of-month payments. The annual rate of interest is 3%. Twenty years from now, you will need to make a 50,000 ending balloon payment. Because you expect your income to increase, you want to structure the loan so at the beginning of each year, your monthly payments increase by 2%. a. Determine the amount of each years monthly payment. You should use a lookup table to look up each years monthly payment and to look up the year based on the month (e.g., month 13 is year 2, etc.). b. Suppose payment each month is to be the same, and there is no balloon payment. Show that the monthly payment you can calculate from your spreadsheet matches the value given by the Excel PMT function PMT(0.03/12,240, 450000,0,0).Consider the linear program max 4y_{1} + 5y_{2} s.t. - y_{1} + y_{2} <= 4 y_{1} - y_{2} <= 10 y_{1}, y_{2} >= 0 (a) Show graphically that the model is unbounded.
- minimize Z = 5x1 + x2 subject to 3x1 + 4x2 = 24 0 x1 x1 + 3x2Yearly oil production in Mexico, and yearly oil imports of the US from Mexico can be represented by the functions: P(t) = 3.0 – 0.13t million barrels I(t) 1.4 + 0.06t million barrels in year t, where t is the time in years since the start of 2000. a) What is represented by the functions P(t) – I(t) and I(t)/P(t)? What are the units for these functions? b) Let q(t) = I(t)/P(t). Compute q'(t) and q'(3). Interpret in a complete sentence. c) In marginal analysis, we would use q' (3) to estimate what quantity? Compute the actual value of that quantity and compare it with q'(3).The relationship between temperature measured on the Celsius scale and on the Fahrenheit scale is linear. The freezing point of water is 0°C and 32°F, and the boiling point is 100°C and 212°F. (a) Find an equation giving the relationship between the temperature F measured on the Fahrenheit scale and the temperature C measured on the Celsius scale.F = (b) Find F as a function of C, and use this formula to determine the temperature in Fahrenheit corresponding to a temperature of 20°C. (Round your answer to one decimal place.)°F(c) Find C as a function of F, and use this formula to determine the temperature in Celsius corresponding to a temperature of 80°F. (Round your answer to one decimal place.)°C
- Define the different components (y, x, a, and b) of a linearregression equationConsider the ordered bases B = space V of upper triangular 2 × 2 matrices. a. Find the transition matrix from C to B. TB = 2 1 -2] and C = for the vector 2 -2 b. Find the coordinates of M in the ordered basis B if the coordinate vector of M in C is [M]c = 22 B [M]B= c. Find M. M =Suppose your total benefits of renting x DVD's next month is: -²2² +14x+50 The cost of renting a DVD is $2, and so the total cost of renting x DVD's is $2x. Calculate your net benefit from watching 1, 2...8 DVDs. Complete column (2). (Enter your responses as integers.) (1) DVDs Rented 0 1 N345678 2 (2) Total Net Benefit
- Determine the pivot element in the simplex tableau. (If there is more than one correct pivot element, choose the element with the smaller row number.) X1 X2 X3 S1 S2 3 4 2 1 15 1 20 -8 -3 10 1 row column N O OMinimization Case. Min C = X1 + X2 + X3Subject toX1 – 3X2 + 4X3 = 5X1 – 2X2 <= 32X2 + X3 >=0And X1, X2, X3 >= 0The initial tableau of a linear programming problem is given. Use the simplex method to solve the problem. X1 X2 S1 S2 S3 1 6. 1. 10 4 1 28 1. 6. -2 -1 The maximum is when x, = x2 = s, = 52 =and sa = n (Type integers or simplified fractions.) %3D ts