The manufacturer of a popular personal computer has orders f

The manufacturer of a popular personal computer has orders from two dealers. Dealer D_1 wants at least 39 computers, and dealer D_2 wants at least 16 computers. The manufacturer can fill the orders from either of two warehouses, W_1 or W_2. There are 31 computers on hand at W_1 and 33 at W_2. The costs to ship one computer to each dealer from each warehouse are shown to the right. Complete parts (a) and (b). How should the orders be filled to minimize shipping costs? Warehouse W_1 should ship [31] computer(s) to dealer D_1 and (33) computer(s) to dealer D_2. Warehouse W_2 should ship [16] computer(s) to dealer D_1 and computer(s) to dealer D_1. The minimum cost will be $|573|.

Solution

Solution (a): We understand the following:

1. D₁ requirement= 39 computers

2. D₂ requirement= 16 computers

so total requirement= 39+16= 55 computers

Now No. of computers available at W1= 31 computers

No. of computers available at W2= 33 computers

Total no. of available computers= 31+33=64 computers

Also we know the following as well:

Cost to ship one computer to any of the dealer i.e D₁or D₂ from W₁=$11

Cost to ship one computer to any of the dealer i.e D₁ or D₂ from W₂=$9

Hence it makes sense to deliver more computers from W₂ & less from W₁ to minimize the cost.

So we will fill the order in following way to minimize the shipping cost:

-33 computers to D₁ from W₂+6 computers to D₁ from W₁+16 computers to D₂ from W₁

Total shipping cost= 33*$9+6*$11+16*$11=$297+$66+$176= $539

Hope this answers your doubt. Please let me know if you need nay furthe rhelp on this. Also Part (b) i smissing in this image so if you need nay help on that, kindly send it over to us.