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Set up and solve Exercises 35–40 by the simplex method.
37. Resource Management The average weights of the three species stocked in the lake referred to in Section 2.2, Exercise 59, are 1.62, 2.14, and 3.01 kg for species A, B, and C, respectively.
- (a) If the largest amounts of food that can be supplied each day are as given in Exercise 59, how should the lake be stocked to maximize the weight of the fish supported by the lake?
- (b) Does it require all of the available food to produce the maximum weight of fish? If not, how much of each type of food is left over?
- (c) Find a value for each of the average weights of the three species that would result in none of species B or C being stocked to maximize the weight of the fish supported by the lake, given the constraints in part (a).
- (d) Find a value for each of the average weights of the three species that would result in none of species A or B being stocked to maximize the weight of the fish supported by the lake, given the constraints in part (a).
59. Fish Food Requirements A lake is stocked each spring with three species of fish, A, B, and C. Three foods, I, II, and III, are available in the lake. Each fish of species A requires an average of 1.31 units of food I, 2.9 units of food II, and 1.75 units of food III each day. Species B fish each require 2.1 units of food I, 0.95 unit of food II, and 0.6 unit of food III daily. Species C fish require 0.86, 1.52, and 2.01 units of I, II, and III per day, respectively. If 490 units of food I, 897 units of food II, and 653 units of food III area available daily, how many of each species should be stocked?
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Chapter 4 Solutions
EBK FINITE MATHEMATICS AND CALCULUS WIT
- Example 3. Food I contains 10 units of vitamin A and 12 unit of vitamin R gram and cost 20 paise per gram. Food II contains 7 unit of vitamin A and 15 unis of vitamin B and costs 18 paise per gram. The daily requirement of vitamin A and R are atleast 80 units and 90 units respectively. Formulate the above as an LPP to per minimise the cost. CS Scanned with CamScannerarrow_forwardIn a laboratory experiment, two separate foods are given to experimental animals. Each food contains essential ingredients, A and B, for which the animals have a minimum requirement; each food also has an ingredient C, which can be harmful to the animals. The table below summarizes this information. Food 1 Food 2 Required Ingredient A 10 units/g 3 units/g 49 units Ingredient B 6 units/g 12 units/g 60 units Ingredient C 3 units/g 1 unit/g How many grams of foods 1 and 2 should be given to the animals to satisfy the requirements for A and B while minimizing the amount of ingredient C ingested? food 1 food 2 ingredient C units Need Help? Read Itarrow_forwardExercise #5arrow_forward
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- A chemical manufacturing plant can produce z units of chemical Z given p units of chemical P and r units of chemical R, where: Chemical P costs $100 a unit and chemical R costs $900 a unit. The company wants to produce as many units of chemical Z as possible with a total budget of $112,500. z = 50p.60.4 A) How many units each chemical (P and R) should be "purchased" to maximize production of chemical Z subject to the budgetary constraint? Units of chemical P, p = Units of chemical R, r = B) What is the maximum number of units of chemical Z under the given budgetary conditions? (Round your answer to the nearest whole unit.) Max production, z= unitsarrow_forwardAn investment club has set a goal of earning 15% on the money it invests in stocks. The members are considering purchasing three possible stocks, with their cost per share (in dollars) and their projected growth per share (in dollars) summarized in the following table. (Let x = computer shares, y = utility shares, and z = retail shares.) Stocks Computer (x) Utility (y) Retail (z) Cost/share 30 44 26 Growth/share 6.00 6.00 2.40 (a) If they have $392,000 to invest, how many shares of each stock should they buy to meet their goal? (If there are infinitely many solutions, express your answers in terms of z as in Example 3.)arrow_forwardAn investment club has set a goal of earning 15% on the money it invests in stocks. The members are considering purchasing three possible stocks, with their cost per share (in dollars) and their projected growth per share (in dollars) summarized in the following table. (Let x = computer shares, y = utility shares, and z = retail shares.) Stocks Computer (x) Utility (y) Retail (z) Cost/share 30 44 26 Growth/share 6.00 6.00 2.40 (a) If they have $392,000 to invest, how many shares of each stock should they buy to meet their goal? (If there are infinitely many solutions, express your answers in terms of z as in Example 3.) (х, у, z) %3D (b) If they buy 900 shares of retail stock, how many shares of the other stocks should they buy? computer shares utility shares What if they buy 1800 shares of retail stock? computer shares utility shares (c) What is the minimum number of shares of computer stock they should buy? shares What is the number of shares of the other stocks in this case? utility…arrow_forward
- An investment club has set a goal of earning 15% on the money it invests in stocks. The members are considering purchasing three possible stocks, with their cost per share (in dollars) and their projected growth per share (in dollars) summarized in the following table. (Let x = computer shares, y = utility shares, and z = retail shares.) Stocks Computer (x) Utility (y) Retail (z) Cost/share 30 44 26 Growth/share 6.00 6.00 2.40 (x, y, z) = (a) If they have $392,000 to invest, how many shares of each stock should they buy to meet their goal? (If there are infinitely many solutions, express your answers in terms of z as in Example 3.) (b) If they buy 500 shares of retail stock, how many shares of the other stocks should they buy? What if they buy 1000 shares of retail stock? (c) What is the minimum number of shares of computer stock they should buy? sharesWhat is the number of shares of the other stocks in this case? (d) What is the maximum number of shares of…arrow_forward22 The Sanders Garden Shop mixes two types of grass seed into a blend. Each type of grass has been rated (per pound) according to its shade tolerance, ability to stand up to traffic, and drought resistance, as shown in the table. Type A seed costs $1 and Type B seed costs $2. If the blend needs to score at least 300 points for shade tolerance, 400 points for traffic resistance, and 750 points for drought resistance, show all your calculations on paper , take a picture, convert to pdf, and upload.Upload your excel file if applicable. Type A Rating Type B Rating Shade Tolerance 1 1 Traffic Resistance 2 1 Drought Resistance 2 5 d. How many pounds of each seed should be in the blend? e. Which targets will be exceeded? f. How much will the blend cost? Please take a picture of all your hand writings and the detail of your work and upload here. Upload all your excel files showing your work here if you have not done so in the previousarrow_forward22 The Sanders Garden Shop mixes two types of grass seed into a blend. Each type of grass has been rated (per pound) according to its shade tolerance, ability to stand up to traffic, and drought resistance, as shown in the table. Type A seed costs $1 and Type B seed costs $2. If the blend needs to score at least 300 points for shade tolerance, 400 points for traffic resistance, and 750 points for drought resistance, show all your calculations on paper , take a picture, convert to pdf, and upload.Upload your excel file if applicable. Type A Rating Type B Rating Shade Tolerance 1 1 Traffic Resistance 2 1 Drought Resistance 2 5 a. Identify decision variables and formulate mathematical statement of objective function based on decisions variables. b. Formulate the constraints in terms of the decision variables. c. Draw the graph with 3 constraint lines and the object line and annotate the graph to identify the optimum. d. How many pounds of…arrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
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