A manufacturer produces three products: Product A, Product B and Product C. To be able to produce each product he uses a combination of three distinct inputs namely Input I, Input II and Input III the supply of which is currently at 730, 350 and 350 units respectively. Each unit of Product A requires 6 units of Input I, 3 units of Input II and 4 units of Input III to be produced. Similarly, each unit of Product B requires 8 units of Input 1 and 4 units of Input II while Product C uses 5 units of Input I, 1 unit of Input II and 3 units of Input III. (i) Let a, b and c represent the number of units produced of Products A, B and C respectively. The manufacturer must decide what quantity of each product to produce so that his entire supply of inputs is utilized. Formulate his/her decision in the form of a system of three linear equations in the variables a, b and c. [3 marks] (ii) Rewrite the above system of linear equations in the matrix form Ax = b.  [2 marks] (iii) Hence or otherwise, determine how many units of product B that can be manufactured   Can you answer all 3 questions please, thank you

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
100%

 A manufacturer produces three products: Product A, Product B and Product C. To
be able to produce each product he uses a combination of three distinct inputs
namely Input I, Input II and Input III the supply of which is currently at 730, 350
and 350 units respectively. Each unit of Product A requires 6 units of Input I, 3
units of Input II and 4 units of Input III to be produced. Similarly, each unit of
Product B requires 8 units of Input 1 and 4 units of Input II while Product C uses 5
units of Input I, 1 unit of Input II and 3 units of Input III.
(i) Let a, b and c represent the number of units produced of Products A, B and C
respectively. The manufacturer must decide what quantity of each product to
produce so that his entire supply of inputs is utilized. Formulate his/her
decision in the form of a system of three linear equations in the variables a, b
and c. [3 marks]
(ii) Rewrite the above system of linear equations in the matrix form Ax = b.
 [2 marks]
(iii) Hence or otherwise, determine how many units of product B that can be
manufactured

 

Can you answer all 3 questions please, thank you 

Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,