Answer:
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.
