Linear programming problem set | Mathematics homework help

Problem 1

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All steel manufactured by Steelco must meet the following requirements: 3.2–3.5% carbon; 1.8–2.5% silicon; 0.9–1.2% nickel; tensile strength of at least 45,000 pounds per square inch (psi). Steelco manufactures steel by combining two alloys. The cost and properties of each alloy are given in Table.

 Alloy 1 Alloy 2 Cost per ton (\$) \$190 \$200 Percent silicon 2 2.5 Percent nickel 1 1.5 Percent carbon 3 4 Tensile strength (psi) 42,000 50,000

Assume that the tensile strength of a mixture of the two alloys can be determined by averaging that of the alloys that are mixed together. For example, a one-ton mixture that is 40% alloy 1 and 60% alloy 2 has a tensile strength of 0.4(42,000) + 0.6(50,000). Use linear programming to determine how to minimize the cost of producing a ton of steel.

Problem 2

Carco Company has a \$150,000 advertising budget. To increase automobile sales, the ?rm is considering advertising in newspapers and on television. The more Carco company uses a particular medium, the less effective is each additional ad. Table 50 shows the number of new customers reached by each ad. Each newspaper ad costs \$1,000, and each television ad costs \$10,000. At most, 30 newspaper ads and 15 television ads can be placed. How can Carco maximize the number of new customers created by advertising?

TABLE 50

Number of Ads New Customers

Newspaper 1–10 900

11–20 600

21–30 300

Television 1–5 10,000

6–10 5,000

11–15 2,000

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