A manufacturer of bicycles builds racing, touring, and mountain models. The bicycles are made of both steel and aluminum. The company has available 57,200 units of steel and 27,600 units of aluminum. The racing, touring, and mountain models need 13, 22, and 26 units of steel, and 9, 21, and 12 units of aluminum, respectively. Complete parts (a) through (d) below. (a) How many of each type of bicycle should be made in order to maximize profit if the company makes $8 per racing bike, $11 per touring bike, and $21 per mountain bike? Let x, be the number of racing bikes, let x₂ be the number touring bikes, and let x3 be the number of mountain bikes. What is the objective function? 2= x₁ + x₂ + x3 (Do not include the $ symbol in your answers.)

A manufacturer of bicycles builds racing, touring, and mountain models. The bicycles are made of both steel and aluminum. The company has available 57,200 units of steel and 27,600 units of aluminum. The racing, touring, and mountain models need 13, 22, and 26 units of steel, and 9, 21, and 12 units of aluminum, respectively. Complete parts (a) through (d) below. (a) How many of each type of bicycle should be made in order to maximize profit if the company makes $8 per racing bike, $11 per touring bike, and $21 per mountain bike? Let x, be the number of racing bikes, let x₂ be the number touring bikes, and let x3 be the number of mountain bikes. What is the objective function? 2= x₁ + x₂ + x3 (Do not include the $ symbol in your answers.)

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter6: Matrices And Determinants

Section6.3: Inverses Of Matrices And Matrix Equations

Problem 63E: Sales Commissions A saleswoman works at a kiosk that offers three different models of cell phones:...

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Sales Commissions A saleswoman works at a kiosk that offers three different models of cell phones: standard with 16 GB capacity, deluxe with 32 GB capacity, and super deluxe with 64 GB capacity. For each phone that she sells, she earns a commission based on the cell phone model. One week she sells 9 standard, 11 deluxe, and 8 super-deluxe and makes $740 in commission. The next week she sells 13 standard, 15 deluxe, and 16 super-deluxe for a $1204 commission. The third week she sells 8 standard, 7 deluxe, and 14 super-deluxe, earning $828 in commission. (a) Let x, y, and z represent the commission she earns on standard, deluxe, and super-deluxe, respectively. Translate the given information into a system of equations in x, y, and z. (b) Express the system of equations you found in part (a) as a matrix equation of the form AX=B . (c) Find the inverse of the coefficient matrix A and use it to solve the matrix equation in part (b). How much commission does the saleswoman earn on each model of cell phone?
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