Thursday

February 26, 2015

February 26, 2015

Posted by **abc** on Friday, December 7, 2012 at 8:24am.

inch plywood. Customer A needs 50 sheets and customer B needs 70 sheets. The east side store has 80 sheets and the west side store has 45 sheets of this plywood in stock. The east side store’s delivery costs per sheet are $0.50 to customer A and $0.60 to customer B. The west side store’s delivery costs per sheet $0.40 to customer A and $0.55 to customer B. How many sheets should be shipped from each store to each customer to minimize delivery costs?

- linear programming math -
**bobpursley**, Friday, December 7, 2012 at 10:07amgo this graphically.

horizontal axis: sheets from East side

vertical axis: sheets from West side

Now, a total of 120 sheets are required. Plot the following line:(120,0 and 0,120)

now you have with the axis, an enclosed area, bounded by x=0 (y axis), y=0 (xaxis) y=45, x=45, and the last line you drew. There is a nice theorem that tells you the optimum solution is at one of the cross marks on the bound of this area. So test points 80,40, and 75,45 for total cost.

Notice the points are on the x,y maximum constraint lines.

so if West provides 45, then East provides 75.

lets consider West sending 45 to A: Then East provides 75 to B: total cost to B is .5*45+.40*5+.55*70=63

What if West sent 45 to B?

total cost=.6*45+.55*15+.40*50=55.25

So, at the point on your graph 75,45 the minimum cost is 55.25.

HOWEVER, there is another point to test, the point (80,40).

consider West sends 40 to A

cost: .5*40+.4*10+.55(70)=62.5

and what if West sends 40 to B..

cost: .6*40+.55*10+.40*70=57.5

so which delivery is mimimum cost?

check my work, please, most of it was done in my head.

**Answer this Question**

**Related Questions**

uthm - 8) A man owns two building supply stores, one on the east side and one on...

math - the figure is made of two identical triangles a 15 inch by 12 inch ...

math - a figure is made up of two identical triangles a 15 inch by 12 inch ...

IRSC - the sum of the lengths of any two sides of a triangle must be greater ...

Stats - The branch manager of an outlet of a nationwide chain of pet supply ...

geometry - There are two noncongruent triangles that have a 9-inch side, a 10-...

geometry - There are two noncongruent triangles that have a 9-inch side, a 10-...

math - Mikhail used 220 inches of wire to make this figure. this figure is made ...

math trigonometry - 1. Two straight roads intersect to form an angle of 75". ...

Geometry - One side of a triangle is x inches longer than another side. The ray...