Answer:
(A) An optimization problem
(B) Variable
(C) $14,700
Explanation:
HOUSTON, PHOENIX, MEMPHIS ----- DALLAS, ATLANTA, DENVER
| | | | | |
850 650 300 800 600 200
Shipping Cost per Room Air Conditioner:
HOUSTON to Dallas - $8 [800 × 8 = $6400]
to Atlanta - $12 [50 × 12 = $600]
to Denver - $10
<em>Total shipping cost = $7,000</em>
<em />
PHOENIX to Dallas - $10
to Atlanta - $14 [250 × 14 = $3500]
to Denver - $9 [200 × 9 = $1800]
<em>Total shipping cost = $5,300</em>
<em />
MEMPHIS to Dallas - $11
to Atlanta - $8 [300 × 8 = $2400]
to Denver - $12
<em>Total shipping cost = $2,400</em>
The total cost of the optimal solution is:
7,000 + 5,300 + 2,400 = $14,700
How was this optimal cost gotten?
- Check the least shipping cost to Dallas, this is found in Houston and that's 8 dollars. Houston hence supplies Dallas 800 ACs and has 50 left. Remember this, in case you need more ACs.
- Check the least shipping cost to Atlanta, this is found in Memphis and that's 8 dollars. An obstruction here is that Memphis only has 300 ACs to send to Atlanta, so Atlanta needs 300 more. Keep this in mind.
- Check the least shipping cost to Denver, this is found in Phoenix and that's 9 dollars. Phoenix hence supplies Denver its needed 200 ACs and has 450 left.
- There is need to complete shipping to Atlanta and the next affordable shipping cost to Atlanta is found in Houston and that's $12. Houston should send its remaining 50 ACs to Atlanta.
- Atlanta needs 250 more ACs and Phoenix has 450 extra. Allen Air Conditioning Company can now settle for the relatively high shipping cost of Phoenix to Atlanta, to supply the remaining 250 ACs which Atlanta needs.
