Summary A contractor, Susan Meyer, has to haul gravel to three building sites. She can purchase as much as 18 tons at a gravel pit in the north of the city.docx

Question 3
A contractor, Susan Meyer, has to haul gravel to three building sites. She can purchase as
much as 18 tons at a gravel pit in the north of the city and 14 tons at one in the south. She
needs 10, 5, and 10 tons at sites 1, 2, and 3, respectively. The purchase price per ton at each
gravel pit and the hauling cost per ton are given in the following table.

Hauling cost per ton at site
Pit 1 2 3 Price per ton
North $30 $60 $50 $100
South $60 $30 $40 $120

Susan wishes to determine how much to haul from each pit to each site to minimize the total
cost for purchasing and hauling gravel. Formulate and solve a linear program for this
problem.

Formulation

Total supply = 18+14 = 32
> Total demand = 10+5+10 = 25

Let Xij = number of tons of gravel from pit i (= 1  North, 2  South) to site j (= 1,2,3)

Min z = 130X11 + 160X12 + 150X13
+ 180X21 + 150X22 + 160X23
s.t.
X11 + X12 + X13  18
X21 + X22 + X23  14

X11 + X21 = 10
X12 + X22 = 5
X13 + X23 = 10

with Xij  0

Solution