Question

XYZ Corporation operates two plants, each of which has a capacity of 100 units per day. Each day, XYZ must ship their product to each of four customers. Customers A, B, and C each have a demand of 20 units per day while customer D has a demand of 140 units per day. The cost of shipping one unit of each product from each of the two plants to each of the customers is shown in the table below. Customer A Customer B Customer C Customer D Plant 1 24 21 19 18 Plant 2 18 16 19 10 How many units should XYZ ship from each plant to each customer? (Leave no cells blank—be certain to enter "0" wherever required. Round your answer to the nearest whole number.) What is the least XYZ will spend on shipping each day? (Round your answers to 2 decimal places.) rev: 07_30_2020_QC_CS

Answer 1

9514 1404 393

Answer:

1. {20, 20, 20, 40} units to {A, B, C, D}
2. {0, 0, 0, 100}

  minimum shipping cost: 3000

Step-by-step explanation:

In general, shipping costs more from Plant 1. The excess costs to ship to customers A, B, C, D are, respectively, (24-18) = 6, (21-16) = 5, (19-19) = 0, (18-10) = 8.

The greatest excess cost is for shipping to customer D from plant 1, so we want to ship as many units as possible to customer D from plant 2.

Shipments from Plant 2 to Customers {A, B, C, D} = {0, 0, 0, 100}.

Then the remaining shipments are fulfilled from Plant 1.

Shipments from Plant 1 to Customers {A, B, C, D} = {20, 20, 20, 40}.

The amount spent on shipping each day is ...

  100×10 +20×24 +20×21 +20×19 +40×18

  = 20×(50 +24 +21 +19 +36) = 3000 . . . . daily shipping cost