A firm has 4 plants that produce widgets. Plants A, B, and C can each produce 100 widgets per day. Plant D can produce 50 widgets per day. Each day the widgets produced in the plants must be shipped to satisfy the demand of 3 customers. Customer 1 requires 75 units per day, customer 2 requires 100 units per day, and customer 3 requires 175 units per day. The shipping costs for each possible route are shown in the table below Shipping Costs per unit Plant Customer
1 2 3
A $25 $35 15
B $20 30 $40
C $40 35 $ 20
D $15 20 25
The firm needs to satisfy all demand each day, but would like to minimize the total costs What is the minimum daily shipping cost that the firm can achieve?
a. $6,725
b. $8,325
c. $7125
d. $7525
e. $7925

A Widgets Firm

Minimization of Shipping Costs to 3 Customers from 4 Locations:

Explanation:

a) Data and Calculations:

Shipping Costs per unit Plant Customer

c. $7125

Plants                                Customers

     Production       1                       2                      3                 Total

Demand units        75 units       100 units          175 units    350 units

A       100 units    $25                $35                  $15

B       100 units    $20                $30                 $40

C      100 units    $40                 $35                 $20

D       50 units     $15                 $20                 $25

To minimize shipping costs:

Satisfy Customer 1's 75 units from B = $20 x 75 =    $1,500

Satisfy Customer 2's 25 units from B = $30 x 25 =       750

Satisfy Customer 2's 25 units from C = $35 x 25 =      875

Satisfy Customer 2's 50 units from D = $20 x 50 =    1,000

Satisfy Customer 3's 100 units from A = $15 x 100 =  1,500

Satisfy Customer 3's 75 units from C = $20 x 75 =    1,500

Daily minimum shipping cost  =                                 $7,125

Minimizing the shipping cost to a location is not considered in isolation. The other locations must be considered.  For example, customer 1's shipping cost would have been minimized to $1,250 instead of $1,500 by shipping D's 50 units and B's 25 units.  But, this would have increased the shipping cost to customer 2 by $500 from $2,625 to $3,125.  Whereas, the company lost $250 shipping to customer 1, it gained $500 shipping to customer 2, thereby making a net gain of $250, instead of net loss of $250.

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