41. Body surface area. Certain chemotherapy dosages depend on a patient's surface area. According to the Mosteller model, Vhw 60 where h is the patient's height in centimeters, w is the patient's weight in kilograms, and S is the approximation of the patient's surface area in square meters. (Source: www.halls.md.) Assume that Kim's height is a constant 165 cm, but she is losing weight. If she loses 2 kg per month, how fast is her surface area decreasing at the in- stant she weighs 70 kg?
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- A high school dietician is planning menus for the upcoming month. Anew item will be spaghetti with sauce. The dietician wants each serving tocontain at least 10 grams of protein and at least 40 grams of carbohydrates.Spaghetti contains 5 grams of protein and 32 grams of carbohydrates per cup,and the sauce contains 4 grams of protein and 5 grams of carbohydrates percup. For aesthetic reasons, the dietician wants a ratio of spaghetti to sauce to be4:1.Spaghetti costs $0.30 per cup to buy and prepare, and the sauce $0.40 per cupto buy and prepare. The dietician wants to minimize the cost per serving andkeep the calories per serving 330 or less. The sauce contains 100 calories percup, and spaghetti contains 160 calories per cup.Formulate a linear programming model for this problem.v The City Council proposed to utilize a government-owned land with an area of 21,600 square meters. One-third of it will be used for a picnic area while the rest of the land will be planted by mango trees. As the city engineer, you were tasked to determine the number of mango trees that leads to a maximum yield given that if 50 trees are planted, the average yield per tree will be 400 kilos while the average yield will decrease by 2 kilos per tree for each additional tree on the same area due to overcrowding. Show a/an: A. Illustration and Representation of Variables B. Detailed SolutionA manufacturer estimates that the cost (C) of production of (x) units of a certain item is ? = 40? − 0.02? − 600. How many units should be produced for a minimum cost?
- A food manufacturing company wants to hire an auditing firm to asses their food safety performance. Two auditing firms are considered: firm A will change 42$/hr and a flat fee of $4500, while firm B will charge 50$/hr with a flat fee of $3900. What is the break-even point in number of required auditing hours that would yield equal value from both companies?The molarity of a solute in solution is defined to be the number of moles of solute per liter of solution (1 mole = 6.02 × 1023 molecules). If X is the molarity of a solution of magnesium chloride (MgCl2), and Y is the molarity of a solution of ferric chloride (FeCl3), the molarity of chloride ion (Cl−) in a solution made of equal parts of the solutions of MgCl2 and FeCl3 is given by M = X + 1.5Y. Assume that X has mean 0.125 and standard deviation 0.05, and that Y has mean 0.350 and standard deviation 0.10. Find μM.if in monopoly market the demand for product is p=1600-x and the revenue is R=px, where x is the number of units sold, what price will maximum revenue?
- Assume the demand for a company's drug Wozac during the current year is 50,000, and assume demand will grow at 5% a year. If the company builds a plant that can produce x units of Wozac per year, it will cost $16x. Each unit of Wozac is sold for $3. Each unit of Wozac produced incurs a variable production cost of $0.20. It costs $0.40 peryear to operate a unit of capacity. Determine how large a Wozac plant the company should build to maximize its expected profit over the next 10 years.An office manager needs to purchase new filing cabinets. He knows that Ace cabinets cost $40.00 each, require 6 square meters of floor space, and holds 8 cubic meters of files. On the other hand, each Excello cabinet costs $80.00, requires 8 meters of floor space and hold 12 cubic meters of files. His budget permits him to spend no more than $560.00 on files, while the office has room for no more than 72 square meters of cabinet. the manager desires the greatest storage capacity within the limitations imposed by the fund and space. 1. how many of each type of cabinet should he buy?The monthly output of a Spanish light bulb factory is P = 2LK2 (in millions), where L is the cost of labor and K is the cost of equipment (in millions of euros). The company needs to produce 1.7 million units per month. Which values of L and K would minimize the total cost L + K?
- Suppose the cost per hour incurred in operating a cruise ship is 5a + b^4v^3 dollars per hour, where a and b are positive constants and v is the ship's speed in miles per hour. At what speed (in miles per hour) should the ship be operated between two ports, at a distance D miles apart, to minimize the cost? (Hint: Minimize the cost, not the cost per hour.) V = _______mphAn environmental landscaping company wishes to run a pipeline from a pumping platform (R) located 40miles offshore to a terminal (B) 15 miles down the coast. It costs $328,000per mile to lay the pipeline underwater and $72,000 per mile to lay the pipeline over land. Determine how many miles from the terminal the two types of pipe should meet (P) so that the total cost is minimized. Enter the exact answer or round to the nearest hundredth.Suppose the production function for an airframe is Q = LK (Quantity = labor x capital) The price of labor is $10 per unit and the price of capital is $1 per unit. Find the cost-minimizing combination of labor and capital if the manufacturer wants to produce 121,000 airframes.