Question

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:.

Answer 1

The minimum daily shipping cost for this firm that will also satisfy all customers is $7125.

How to find the minimum shipping cost?

Analyze which shipping option is better for each customer based on the number of units required and costs.

Customer A:

• Units required: 75 units                  
• Best option: Plant
• Total cost: 75 x 20 = $1,500

Customer B:

• Units required: 100 units
• Best option: Plant B and C (25 units each), and plant D (50 units)
• Total cost: ($30 x 25=$750)+ ($35 x 25 = $875)  ($20 x 50 =  $1,000) =$2625

Customer C:

• Units required:  175 units
• Best option: Plant A (100 units) and C (75 units)
• Total cost: ($15 x 100 = $1,500) + ($20 x 75 = $1,500) = $3,000

Total: $1,500 + $2,625 + 3,000 = $7,125

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