Linear programming problem set | Mathematics homework help


Problem 1

All steel contrived by Steelco must coalesce the aftercited requirements: 3.2–3.5% carbon; 1.8–2.5% silicon; 0.9–1.2% nickel; tensile force of at last 45,000 pounds per balance inch (psi). Steelco manufactures steel by combining two decrements. The require and properties of each decrement are absorbed 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 force (psi)

42,000

50,000

Assume that the tensile force of a conformation of the two decrements can be rooted by averaging that of the decrements that are adulterated contemporaneously. For model, a one-ton conformation that is 40% decrement 1 and 60% decrement 2 has a tensile force of 0.4(42,000) + 0.6(50,000). Use rectirectilinear programming to individualize how to minimize the require of unresisting a ton of steel.

 

Problem 2

Carco Order has a $150,000 advertising budget. To extension automobile sales, the ?rm is because advertising in newspapers and on television. The past Carco order uses a point balance, the close talented is each concomitant ad. Table 50 shows the compute of new customers reached by each ad. Each newspaper ad requires $1,000, and each television ad requires $10,000. At most, 30 newspaper ads and 15 television ads can be placed. How can Carco maximize the compute 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

 

Problem 3

Juiceco manufactures two products: bribe orange-colored-colored-colored juice and orderly orange-colored-colored-colored juice. Both products are made by combining two types of orange-colored-coloreds: space 6 and space 3. The orange-colored-coloreds in bribe juice must keep an mean space of at last 5, those in orderly juice, at last 4. During each of the direct two months Juiceco can vend up to 1,000 gallons of bribe juice and up to 2,000 gallons of orderly juice. Bribe juice vends for $1.00 per gallon, conjuncture orderly juice vends for 80¢ per gallon. At the foundation of month 1, Juiceco has 3,000 gallons of space 6 orange-colored-coloreds and 2,000 gallons of space 3 orange-colored-coloreds. At the foundation of month 2, Juiceco may donation concomitant space 3 orange-colored-coloreds for 40¢ per gallon and concomitant space 6 orange-colored-coloreds for 60¢ per gallon. Juice prey at the end of the month, so it shapes no notion to shape extra juice during month 1 in the hopes of using it to coalesce month 2 insist. Oranges left at the end of month 1 may be used to fruit juice for month 2. At the end of month 1 a avocation require of 5¢ is assessed athwart each gallon of leftover space 3 orange-colored-coloreds, and 10¢ athwart each gallon of leftover space 6 orange-colored-coloreds. In observation to the require of the orange-colored-coloreds, it requires 10¢ to fruit each gallon of (orderly or bribe) juice. Formulate an LP that could be used to maximize the gain? (revenues requires) earned by Juiceco during the direct two months.