Cost analysis. A company with two different plants manufactures guitars and banjos. Its production costs for each instrument are given in the following matrices.Plant XMaterialsLaborFind (A + B), the average cost of production for the two plants.(A+B) =Guitar(Type integers or decimals.)$43 $40$92 $116BanjoGuitarPlant Y$57 $38$128 $122Banjo

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Answered: Cost analysis. A company with two…

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 small software corporation borrowed $315,000 to expand its software line. The corporation borrowed some of the money at 3%, some at 4%, and some at 5%. Use a system of equations to determine how much was borrowed at each rate when the annual interest was $13,500 and the amount borrowed at 4% was 22/12/2012 times the amount borrowed at 3%. Solve the system using matrices. amount borrowed at 3% $ amount borrowed at 4% $ amount borrowed at 5% $
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…
Protein(g) Carbohydrates(g) Sodium(mg) Cost($) DesignerWhey (Next) 18 2 80 0.50 Muscle Milk(Cytosport) 32 16 240 1.60 Pure WheyProtein Stack(Champion) 24 3 100 0.60 You are thinking of combining Designer Whey and Muscle Milk to obtain a 7-day supply that provides exactly 430 grams of protein and 110 grams of carbohydrates. How many servings of each supplement should you combine in order to meet your requirements?
An economy consists of coal, electric, and steel industries. For each $1.00 of output, the coal industry needs $0.01 worth of coal, $0.20 worth of electricity, and $0.20 worth of steel; the electric industry needs $0.02 worth of coal, $0.04 worth of electricity, and $0.03 worth of steel; and the steel industry needs $0.30 worth of coal and $0.02 worth of steel. The sales demand is estimated to be $1 billion for coal, $3 billion for electricity, and $4 billion for steel. Suppose that the demand for electricity triples and the demand for coal doubles, whereas the demand for steel increases by only 50%. At what levels should the various industries produce in order to satisfy the new demand? Set up the input-output matrix. Coal Electric Steel Coal 0.01 0.02 0.30 Electric Steel 0.20 0.04 0.20 0.03 0 0.02 The coal industry should produce $ ☐ billion the electric industry should produce $ ☐ billion, and the steel industry should produce $ (Round the final answer to the nearest billion as…
A farmer owns 100 hectares of land to grow crops A, B, and C. The costs to grow crops A, B, and C per hectare are $ 40, $ 60, and $ 80, respectively. The farmer has 12,000 dollars in planting costs. The energy needed to cultivate plants A, B, and C per hectare is 10 hours of work, 15 hours of work, and 20 hours of work, respectively. The farmer has 4,000 hours available. The farmer wants to use all the land, all the budget for planting costs, as well as all available labor.a. Model a system of linear equations for the problem using a matrix representation!b. Solve the system of linear equations by eliminating Gauss or Gauss-Jordan to determine the area of land to plant each crop.!
A small software corporation borrowed $292,500 to expand its software line. Some of the money was borrowed at 9%, some at 10%, and some at 12%. Use a system of equations to determine how much was borrowed at each rate if the annual interest was $29,900 and the amount borrowed at 10% was 22 times the amount borrowed at 9%. Solve the system using matrices. Step 1 Let the amount borrowed at 9% be x, the amount borrowed at 10% be y, and the amount borrowed at 12% be z. The total amount borrowed was $292,500. The total annual interest was $29,900. The amount borrowed at 10% was 2- times the amount borrowed at 9%. Write a set of equations using the information given. Convert the percentage to decimal fraction. x + y + z = 292,500 .09 x +.10 y + |.12 V z = 29,900 X x - y = 0 Write the associated augmented matrix for the given system of equations. Recall that since there are three equations in the system, the matrix will have three rows. Use the coefficients of x, y and z as entries of the…

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