Two departments of a firm, A and B, need differing amounts of steel, wood, and plastic. The table on the right gives the amount of each product the departments need.These three products are supplied by two suppliers, Company C and Company D, with the unit prices given in the table on the right.Ca. Use matrix multiplication to determine how much these orders will cost each department at each of the two suppliers. Enter the amounts into the cost matrixshown on the right.Dept. ADept. BDepartment ADepartment BSteelWoodPlasticCo. CCompany C580280280Co. DCompanyD—570180380Steel7060Wood6040Plastic4060

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Answered: Two departments of a firm, A and B,…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A patient takes vitamin pills. Each day he must have at least 900 IU of vitamin A, 14 mg of vitamin B₁, and 80 mg of vitamin C. He can choose between pill 1, which contains 180 IU of vitamin A, 2 mg of vitamin B₁, and 10 mg of vitamin C, and pill 2, which contains 90 IU of vitamin A, 2 mg of vitamin B₁, and 15 mg of vitamin C. Pill 1 costs 25¢, and pill 2 costs 75¢. Complete parts a and b below. a. How many of each pill should he buy in order to minimize his cost? What is the minimum cost? He should buy 8 of pill 1 and 0 of pill 2. The minimum cost is $ 2. (Simplify your answers. Type integers or decimals.) b. For the solution in part a, the patient is receiving more than he needs of at least one vitamin. Identify that vitamin, and tell how much surplus he is receiving. mg of vitamin C more than he needs. and He is receiving IU of vitamin A, mg of vitamin B₁, a (Simplify your answers.)
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…
b. Number of boys and girls in each block: Let's say you want to graph the number of boys and girls in each grade level in a school. You have five grade levels: kindergarten, first grade, second grade, third grade, and fourth grade. In kindergarten, there are 15 boys and 10 girls. In first grade, there are 20 boys and 18 girls. In second grade, there are 12 boys and 14 girls. In third grade, there are 16 boys and 20 girls. In fourth grade, there are 18 boys and 16 girls.Make an appropriate graph for this situation in EXCELShow the steps on how you made it
A small company manufactures three different electronic components for computers. Component A requires 2 hours of fabrication and 1 hour of assembly; component B requires 3 hours of fabrication and 1 hour of assembly; and component C requires 2 hours of fabrication and 2 hours of assembly. The company has up to 900 labor-hours of fabrication time and 700 labor-hours of assembly time available per week. The profit on each component, A, B, and C, is $7, $8, and $10, respectively. How many components of each type should the company manufacture each week in order to maximize its profit (assuming that all components manufactured can be sold)? What is the maximum profit? Let x₁, x2, and x3 be the numbers of components A, B, and C, respectively, that get manufactured. Construct a mathematical model in the form of a linear programming problem. Maximize P=[ subject to X1, X₂, X3 20 The company should manufacture (Simplify your answers.) Fabrication time restriction Assembly time restriction…
The per-unit amount of three different production costs for Thunderbird, Inc., are as follows: Cost A(per unit) Cost B(per unit) Cost C(per unit) Production = 16,000 $32 24 $19.20 Production = 64,000 $8 8.00 $19.20 What type of cost is each?
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…
Q: The Morton Supply Company produces clothing, footwear, and accessories for dancing and gymnastics. They produce three models of pointe shoes used by ballerinas to balance on the tips of their toes. The shoes are produced from four materials: cardstock, satin, plain fabric, and leather. The number of square inches of each type of material used in each model of shoe, the amount of material available, and the profit/model are shown below: Material (measured in square inches) Model 1 Model 2 Model 3 Material Available Cardstock 12 10 14 1200 Satin 24 20 15 2000 Plain fabric 40 40 30 7500 Leather 11 11 10 1000 Profit per model $50 $44 $40 a) Generate the Answer Report using SOLVER in EXCEL. Then, clearly answer what is the optimal solution? What is the resulting profit? b) Generate the Sensitivity Report for the model that you built. Interpret, in context, the Shadow Price for the Leather and the Satin constraints. Include units in your interpretations.
The owner of an apartment building can rent all 50 apartments if she charges $1,700 per month, but she rents one fewer apartment for each $50 increase in monthly rent. (a) Construct a table that gives the revenue generated if she charges $1,700, $1,750, and $1,800. Total Revenue No. of Apts 50 49 48 Rent $1,700 $ 85000 $1,750 $ 85750 $1,800 $ 86400 Need Help? ✓ Excellent job! (b) Does her revenue from apartment rentals increase or decrease as she increases the rent from $1,700 to $1,800? o revenue increases revenue decreases Read It ✓ Great job. ✓ Way to go! Nice work. (c) Write an equation that gives the revenue R, from apartment rentals if she makes x increases of $50 in the rent. R(x) = -50x² +800x+8500 X (d) Find the rent she should charge to maximize her revenue. $2100 ✓per month

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