SOLUTION: a stereo manufacturer has two warehouses labeled I and II. Warehouse I has nine speakers in stock while warehouse II has five. The manufacturer receives orders from customer a for

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Question 1106875: a stereo manufacturer has two warehouses labeled I and II. Warehouse I has nine speakers in stock while warehouse II has five. The manufacturer receives orders from customer a for 7 speakera and from customer b for 6 speakers. the shipping rates to send one speaker to cust a is $11 from warehouse and $15 from warehouse II. Cost for customer B is $12 per speaker from warehouse I and $13 from warehouse II. How many speakers should be sent from each warehouse to each customer so that the order is filled for the smallest cost?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
make a cost matrix like the one shown below: 
                           warehouse 1       warehouse 2

     customer A               11                15
     customer B               12                13


the maximum number of speakers from warehouse 1 is 9.
the maximum number of speakers from warehouse 2 is 5.

it's clear from this matrix that the minimum cost to ship to customer A is from warehouse 1.

since customer A requires 7 and warehouse 1 has 9, then ship all stereos to customer A from warehouse 1.

since the cost to ship to customer B is cheaper from warehouse 1, then ship the remaining 2 that warehouse 1 has to customer B.

the remaining 4 that customer B requires is then shipped from warehouse 2.

your total cost will be:

7 from warehouse 1 to customer A = 77
2 from warehouse 1 to customer A = 24
4 from warehouse 2 to customer B = 52

total cost is 153.

the cheapest cost to ship is 153.

i then double checked to see if my logic was correct.

i used excel solver.

excel confirmed that my logic was correct.

it came up with the same minimum cost.

the variables that i used were:

xa = amount shipped from warehouse 1 to customer a.
xb = amount shipped from warehouse 1 to customer b.
ya = amount shipped from warehouse 2 to customer a.
yb = amount shipped from warehouse 2 to customer b.

the objective function which i wanted to minimize was:

xa * 11 + xb * 12 + ya * 15 + yb * 13

this objective function represented the total cost of shipping.

my constraints were:

xa + ya = 7 because customer a required 7 speakers.
xb + yb = 6 because customer b required 6 speakers.

xa + xb <= 9 because warehouse 1 could ship a maximum of 9 speakers.
ya + yb <= 5 because warehouse 2 could ship a maximum of 5 speakers.

here's a picture of my excel spreadsheet.

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