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![find the average Value
of the function.
f(x):
=
2
X -11 on
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- You will enter each part of this problem over the next few questions. A manufacturer of basketball shoes makes shoes using leather, nylon, rubber, and labor. The company makes two models, the Dunker and the Flyer, Each pair of Dunker shoes requires 6 ounces of leather, .6 square feet of nylon, 10 ounces of rubber, and 7 minutes of labor. Each pair of Flyer shoes requires 8 ounces of leather, 4 square foot of nylon, 12 ounces of rubber, and 9 minutes of labor. The company has 20 pounds of leather, 150 square feet of nylon, 50 pounds of rubber, and 20 hours of labor. The profit per pair is $16 for the Dunker and $24 for the Flyer. How many pairs of each type of shoe should the company produce to achieve maximum profit? Let x number of Dunker, y = number of Flyer 06+8≤320 O6x+8y 2320 Submit Answer 6x-8y < 32 6x+8y320 OThe research department at a manufacturing company has developed a new process that it believes will result in an improved product. Management must decide whether to go ahead and market the new product. The new product may or may not be better than the old one. If the new product is better and the company decides to market it, sales should increase by $70,000. If it is not better and they replace the old product with the new product on the market, they will lose $25,000 to competitors. If they decide not to market the new product, they will lose a total of $60,000 if it is better and just research costs of $20,000 if it is not. Complete parts (a) and (b) below. (a) Prepare a payoff matrix. □ (Type an integer or decimal for each matrix element. Do not include the $ symbol in your answer.)USA. Benjamin Banneker (1731-1806) is one of the great American heroes of all time. The son and grandson of Africans captured and enslaved, he was fortunate to have been born free. He inherited the family farm where he worked hard all of his life. As a child he had a few months of schooling. Everything else he had to do on his own. He loved mathematics and science but did not get a chance to learn astronomy until he was in his fifties. Then he performed a near miracle, learning it all in less than a year. In his hand-written journal, he recorded two right triangle examples that interested him. You can solve them here and remember the great man who enjoyed geometry. On the page in his journal next to the August 1775 astronomy calculations, Banneker wrote, in the style of that time: Suppose a ladder 60 feet long be placed in a Street so as to reach a window on the one Side 37 feet high, and without moving it at bottom, will reach another window on the other side of teh Street which is 23…
- After running a mile a day over a period of two weeks, the average amount of weight loss is 2.5 pounds. A dietitian, who publishes health articles in a newspaper, states their new diet program helps with additional weight loss when combining their special diet with running a mile a day over a period of two weeks. Interested in studying the dietitian's article further, you ask friends who have tried the dietitian's new program and you determine their weight loss to be 3.0 pounds in a two-week period, on average. As you set up a hypothesis test to determine if the dietitian's article is correct, what is the dietitian's claim?John wishes to choose a combination of two types of cereals for breakfast - Cereal A and Cereal B. A small box (one serving) of Cereal A costs $0.45 and contains 10 units of vitamins, 5 units of minerals, and 15 calories. A small box (one serving) of Cereal B costs $0.40 and contains 5 units of vitamins, 10 units of minerals, and 15 calories. John wants to buy enough boxes to have at least 450 vitamins, 525 minerals, and 1125 calories. How many boxes of each food should he buy to minimize cost, and what is the minimum cost? To minimize his cost. John should buy minimum cost would be boxes of Cereal A and boxes of Cereal B. TheThe table on the right shows the calories, sodium, and protein in one cup of various kinds of soup, How many cups of each kind of soup should be mixed together to produce 10 servings of soup, each of which provides 186 calories, 954 milligrams of sodium, and 13.2 grams of protein? What is the serving size (in cups)? Calories Sodium (mg) Protein (g) Chicken NoodleChicken & RiceChicken Rotini 100 130 520 730 7 9 110 530 8 To produce 10 servings of soup, each of which provides 186 calories, 954 milligrams of sodium, and 13.2 grams of protein, mix cups of Chicken Noodle, cups of Chicken & Rice, and cups of Chicken Rotini.
- You are opening a plant that will manufacture widgets (w) and gizmos (g). The widget machines cost $10,000 each. They each require 4 operators and 500 square feet o space. The gizmo machines each cost $6,000 ard require 6 operators and 500 square feet of space. Your new plant has 40,000 square feet of space available for the machines. HR estimates that you will be able to hire 460 operators to run the machines. Your budget for buying machines is $660,000. a) List all 5 constraints. b) List the coordinates of the corners of the graph in (g,w) form. (We cannot buy a fraction of a production machine. If the corners are not whole numbers, give the closest whole number coordinates along each constraint line.) c) Given the following estimated profits per hour per machine in each scenario, how many of each type of machine should you buy? What will be your profit per hour at tha Profit per Maximum Profit per Widget Number of Gismos Number of Widets Gizmo Profit $99 $98 $78 $120 $265 $103 ts…A company produces widgets at plants 1 and 2. It costs 125x1y2 dollars to produce x units at plant 1 and 235x1y3 dollars to produce x units at plant 2.Each plant can produce up to 500 units. Each unit produced can be sold for $10. At most 800 widgets can be sold. Determine how -the company canmaximize its profit.Every February, Francine's Flowers packages bouquet for Valentine's The smaller bouquets consist of two Stargazs Liles, three Gardenia and five Alstroemerias and sells for $15.75 The larger bouquet has 6 Alstroernerias, 4 Gardenia and 8 Stargazer Lilies and sells for $34 The cost of producing the bouquets is $6.25 for the small bouquet and $16 for the large bouquet a Formulate a linear programming model that will help Francine decide on the number of bouquets or each size to package to minimize her costs. Do Not Solve. b Formutate a linear progranming model that will help Francine decide on the number of bouquets of each size to package to maxirmize her profits Do Not Solve
- A researcher believed that the number of rental cars in service by a car rental company would have an impact on the total annual revenue for that car rental company. Five small car rental companies were surveyed, with the number of Cars in service recorded in units of 1000 (so if a car rental company had 54000 cars in service, a 54 would be recorded) and Annual Revenue measured in millions of dollars (so an Annual Revenue of $10,000,000 would be recorded as 10). The data follows: Cars (1,000s) Annual Revenue ($ millions)11.5 118 10.0 135 9.0 100 5.5 37 3.3 32 Part of the Excel-generated Simple Linear Regression output is provided below: ANOVA df SS MS F Significance F Regression 1 7891.863897 7891.863897 22.91180151 0.017339231 Residual 3 1033.336103 344.4453677 Total 4 8925.2 Coefficients Standard Error t Stat P-value Intercept -19.12490108 23.1658578…Direction: Analyze the given problem and show your complete and detailed solution using multiplication priniciple. A special plate number is made of three letters in the English Alphabet followed by two-digit numbers. How many plate numbers are possible if (a) the digits and letters can be repeated in the same plate number (b) the letters and digits cannot be repeated in the same plate number.For the remainder of this question, we will consider one of the world's most popular video games, Minecraft (adapted from Mills & Mills, 2016). In this game, the character (you) can attempt to tame a wolf with a bone. Assume that you get 9 tries to tame the wolf, i.e. there are 9 bones. Each time you tame the wolf, the wolf becomes a dog and a new wolf appears which you can then attempt to also tame. This continues until you have used up all 9 bones, and the goal is to end up with as many dogs as possible at the end of the game. The probability of taming the wolf with each attempt is fixed at 0.54. Let X denote the number of dogs at the end of the game so that X~ BIN (9,0.54). Assume you are about to play the game. 15. The probability that you will tame some number a or less dogs is 0.66144. What must be (round to the nearest whole number)?
