Linear Equations – Assembly Manufacturing Process

Linear Equations Applied to Manufacturing Process

Pandora Vehicle Sdn. Bhd. produces two models of bicycles: model A and model B.

     • Assembly Time.

         - Model A requires 2 hours of assembly time.

         - Model B requires 3 hours of assembly time.

     • Cost of Parts.

         - The parts for model A cost RM25 per bike

         - the parts for model B cost RM30 per bike

     • Time and Money Budgeted to produce these two models

         - total of 34 hours of assembly time per day

         - RM365 is available per day

How many of each model can be made in a day?

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Sep 03, 2012

Linear Equations Applied to Manufacturing Process
by: Staff

Answer:

Part I

A = number of Model A bicycles manufactured

B = number of Model B bicycles manufactured

T = total number of bicycles (A + B) manufactured

The objective function:

     • maximize total units manufactured:

       T = A + B

Constraints

     • Equation which models Assembly Time:

         - maximum time available = 34 hours per day

         - Model A requires 2 hours of assembly time.

         - Model B requires 3 hours of assembly time.

       (2 hours) * (number of Model A bicycles) + (3 hours) * (number of Model B bicycles) ≤ 34 hours

       2A + 3B ≤ 34

     • Equation which models the Cost of Parts:

         - maximum cost cannot exceed RM365 per day

         - Model A requires parts which cost RM25.

         - Model B requires parts which cost RM30.

       (RM25) * (number of Model A bicycles) + (RM30) * (number of Model B bicycles) ≤ RM365

       25A + 30B ≤ 365

Mathematically, the question before us is:

     • Solve for the values of A and B which maximize the following objective function :

         T = A + B

     • Subject to the following restrictions:

         2A + 3B ≤ 34

         25A + 30B ≤ 365

         A ≥ 0

         B ≥ 0

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Sep 03, 2012

Linear Equations Applied to Manufacturing Process
by: Staff

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Part II

Plot the restrictions:

         2A + 3B ≤ 34
         (the red line and all the area below the red line)

         25A + 30B ≤ 365
         (the green line and all the area below the green line)

         A ≥ 0
         (all the area to the right of the vertical blue line, which is the “B-axis”)

         B ≥ 0
         (all the area above the horizontal pink line, which is the “A-axis”)

     • When these boundaries are plotted, the area inside the boundaries forms the Bounded Feasible Region:

         Bounded Feasible Region
         (shaded yellow area)

$Math – graph of linear equations for assembly manufacturing$

• The corner points of the bounded feasible region (shown as the yellow shaded area) define a maximum value and a minimum value for the objective function (T = A + B).

$Math – corner points of the bounded feasible region$

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Sep 03, 2012

Linear Equations Applied to Manufacturing Process
by: Staff

---------------------------------------------

Part III

     • The corner points are (in A,B format):

         (0,0), (0,11⅓), (5,8), (14.6,0)

     • Find the maximum value of T by computing the values of T at the corner points.

         T = A + B

       Corner point: (0,0)

         T = 0 + 0 = 0, minimum value of T

       Corner point: (0,11⅓)

         T = 0 + 11⅓ = 11⅓

       Corner point: (5,8)

         T = 5 + 8 = 13

       Corner point: (14.6,0)

         T = 14.6 + 0 = 14.6, maximum value of T

       Maximum value of T is: 14.6; when A = 14.6 and B = 0

       Minimum value of T is: 0; when A = 0 and B = 0

Final Answer

Maximum possible Number of A units = 14

Maximum possible Number of B units = 11

Maximum possible Number of TOTAL units = 14

Thanks for writing.

Staff
www.solving-math-problems.com

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Linear Equations – Assembly Manufacturing Process

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