Question

Suppose that chemical X is manufactured using a raw material B that is available from a location called the "mine." Production of one ton of X requires 1/3 of a ton of B. A firm called X Enterprises, which has a contract to deliver 30 tons of X to a location called the "market," is trying to decide where to locate its plant. The mine and the market are 50 miles apart. river passes between the mine and the market, and the river has no bridge. Goods must be loaded onto barges to cross the river, which is located 16 miles from the mine. Barge operators charge $1 per ton of X shipped across the river. However, since the input B is highly toxic when mixed with water, barge operators must charge an extremely high price to transport B across the river. This price defrays the cost of insurance that the operators must carry to meet liability claims should they accidentally pollute the river with their cargo. The cost of shipping one ton of B across the river is $195. Four locations for frms are: mine, market, mine side of the river, and market side of river (1) Using the above information, find the transport-cost-minimizing location for X Enterprises, which is the location (Assume that the width of the river is negligible so that it can be ignored.) (2)The input cost of the location you flled in above for the firm is , and the output cost is , and the total cost is

Answer 1

Given data;

Manufactured chemical=X,

Raw material=B

The production of 1 ton of X is requires 1/3 of a ton B

X contract deliver=30 tons

the mine and market are apart=50 miles apart

the barge operator charge=$1 ton of X shipped across the river

the cost of shipping=1 ton of B

the one ton B across the river=$195

(1) THE TRANSPORT-COST-MINIMIZING LOCATION:

we know that,

the cost delivering formula is

Cost of delivering 30 tons of X = Overland cost + Cost of crossing river

MINE: (30*2*50)+(1*30)

= 3000+30

= $ 3030

MINE=$3030

MARKET:

   (10*2*50)+(195*10)

= 1000+1950

= $ 2950

MARKET=$2950

MINE SIDE OF RIVER:

((10*2*16)+(30*2*34))+(1*30)

= (320+2040)+ 30

= $2390

MARKET SIDE OF RIVER:

((10*2*16)+(30*2*34))+(195*10)

= (320+2040)+ 1950

= $4310

Hence, the location that minimizes transport cost is MINE SIDE OF RIVER.

(2) Input cost:

=10*2*16

= $320

Output cost:

=30*2*34+1*30

= $ 2070

Total cost:

total cost= input cost+output cost

=320+2070

= $2390

TOTAL COST=$2390