Summary 745Los Angeles New Orleans New York
Oregon $14 $26 $30
Tennessee 24 10 12The maximum capacity of the Oregon plant is 9,000 tons; the
capacity of the Tennessee plant is 10,000 tons. The minimum daily
quantities shipped overseas from Los Angeles, New Orleans, and New
York are 5,000, 7,000, and 6,000 tons, respectively.
a. The company’s objective is to minimize the cost of transporting its
product from plants to ports while fulfilling its daily overseas shipping
requirements. Formulate the appropriate LP problem.
b. Attempt to solve the LP problem by inspection. Find the company’s
minimum-cost transport plan using a standard LP computer program.
c. Find and interpret the shadow price associated with the 6,000
minimum daily shipment to New York.
S2. A manufacturer produces six products from six inputs. Each product
requires different combinations and amounts of inputs. The following
table shows the profit and raw materials requirements for each product.
The last column shows the total amounts of raw materials available.Total Amounts
Products 1 2 3 4 5 6 of Inputs
Profits 60 70 48 52 48 60
Inputs Required:
Aluminum .5 2 — 2 1 — 400
Steel 2 2.5 1.5 — .5 — 580
Plastic — 1.5 4 — .5 — 890
Rubber 1 — .5 1 .5 2.5 525
Glass 1 2 1.5 .4 1 2 650
Chrome .5 2 .5 2 1.5 2 620a. Formulate the appropriate linear program.
b. Find the company’s most profitable production plan using a
spreadsheet optimizer.
S3. The accompanying spreadsheet lists six different means of generating
electricity in the United States. Row 6 lists the estimated megawatt hours
produced in 2010 by power plants of each kind. In turn, row 7 lists the
maximum capacity for each, while row 9 shows the proportion of the US
total (3.8 billion MWh) for each source. (For instance, coal-burning
facilities account for 46 percent of electricity generation.) As discussedc17LinearProgramming.qxd 9/26/11 11:05 AM Page 745