Question

Best Brands Appliance Mart is getting ready for its annual Labor Day sale. There are two Best Brands stores, one in midtown Manhattan and another in Amityville. Merchandise is stored in two warehouses, one in Brooklyn and one in Baldwin. From experience in past years, the owners know the big mover during the sale is tablets. The Manhattan store needs 500, while the Amityville store will require 400. Each warehouse has 600 tablets in stock. It costs $1 and $2 to ship a tablet from Brooklyn to Manhattan and to Amityville, and $2 and $4 to ship one from Baldwin to Manhattan and Amityville. What is the best shipping strategy for getting the tablets from the warehouses into the stores to minimize the shipping cost?

Answer 1

Answer:

Explanation:

From the given information:

Assuming we represent x to be the tablets sent from Brooklyn to Manhattan

Thus, (500 - x) to be the tablets sent from Baldwin to Manhattan

Also, suppose we represent y to be the tablets sent from Brooklyn to Amityville

It implies that (400 - x) to be the tablets sent from Baldwin to Amityville

∴

x ≥ 0 ; y ≥ 0  

⇒   500 - x ≥ 0  & 400 - y ≥ 0

The Shipping cost Z = 1(x) + 2(500-x) + 2(y) + 4(400-y)

Z = x + 1000 - 2x + 2y + 1600 - 4y

Z = x -2y + 2600

To minimize the shipping cost:

$\left \{ 500-x \geq 0 \ \implies \ x\leq 500}} \atop {400-y \geq 0 \ \implies \ y\leq 400}} \right.$

Thus, by replacing the coordinate values (x,y) into Z, we have:

Point    Coordinates(x,y)    Value of Z (shipping cost)

0             (0,0)                             0

A             (0,400)                     1800

B             (500,400)                 1300

C             (500,0)                      2100

Hence, the minimum cost is 1300.

x = 500 units   and  y = 400 units