5. A steel company has two mills. Mill 1 costs $70,000 per day to operate, and it canproduce 400 tons of high-grade steel, 500 tons of medium-grade steel, and 450 tons oflow-grade steel each day. Mill 2 costs $60,000 per day to operate, and it can produce 350tons of high-grade steel, 600 tons of medium-grade steel, and 400 tons of low-grade steeleach day. The company has orders totaling 100,000 tons of high-grade steel, 150,000 tonsof medium-grade steel, and 124,500 tons of low-grade steel. Use the Simplex technique(do not use excel show workings) to find out how many days the company should runeach mill to minimize its costs and still fill the orders.

Given, that Mill costs per day to operate.Mill costs per day to operate.Production capabilities…

Answered: A steel company has two mills. Mill 1…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A company manufactures paring knives and pocket knives. Each paring knife requires 3 labor-hours, 7 units of steel, and 4 units of wood. Each pocket knife requires 6 labor-hours, 5 units of steel, and 3 units of wood. The profit on each paring knife is $3, and the profit on each pocket knife is $5. Each day the company has available 90 labor-hours, 156 units of steel, and 117 units of wood. Suppose that the number of labor-hours that are available each day is increased by h. For what values of h will a change of h labor-hours not change the shadow price of labor? The shadow price of labor will not change for shs. (Simplify your answers.)
You are in charge of purchases at the student-run used-book supply program at your college, and you must decide how many introductory calculus, history, and marketing texts should be purchased from students for resale. Due to budget limitations, you cannot purchase more than 1000 of these textbooks each semester. There are also shelf-space limitations: Calculus texts occupy 2 units of shelf space each, history books 1 unit each, and marketing texts 2 units each, and you can spare at most 1,600 units of shelf space for the texts. If the used book program makes a profit of $20 on each calculus text, $8 on each history text, and $16 on each marketing text, how many of each type of text should you purchase to maximize profit?
A factory manufactures three products, A, B, and C. Each product requires the use of two machines, Machine I and Machine II. The total hours available, respectively, on Machine I and Machine Il per month are 7,090 and 10,940. The time requirements and profit per unit for each product are listed below. A B C Machine I 5 8 10 Machine II 10 9 16 Profit $10 $13 $18 How many units of each product should be manufactured to maximize profit, and what is the maximum profit? Start by setting up the linear programming problem, with A, B, and C representing the number of units of each product that are produced. Maximize P = subject to: ≤7,090 ≤ 10,940 Enter the solution below. If needed round numbers of items to 1 decimal place and profit to 2 decimal places. The maximum profit is $ units of product A units of product B units of product C when the company produces:
Consider the town of Acaford with a population of 5,000 people. There are 1,000 high school students, 1,000 undergraduate students, 1,000 graduate students, 1,000 economics professors, and 1,000 retired economists. Suppose that the total annual income in the economy is $100 million: Each high school student earns $6,000 annually; each undergraduate earns $10,000 annually; each graduate student earns $25,000 annually; each professor earns $55,000 annually; and each retiree earns $4,000 annually. The following chart shows the income distribution for the town of Acaford. 60 50 40 30 20 10 High SchoolUndergrads Grads Profs Retirees Suppose that the government sets the poverty line at an annual income of $18,000. The percentage of people with annual incomes below the poverty line in Acaford is 20%, 40%, 60% 80% Which of the following sequences correctly orders the people of Acaford from the bottom fifth to the top fifth of income distribution? SHARE OF TOTAL INCOME (Percent) 2)
An oil company has two refineries. Each day, Refinery A produces 200 barrels of high-grade oil, 300 barrels of medium-grade oil, and 200 barrels of low-grade oil and costs $12,000 to operate. Each day, Refinery B produces 100 barrels of high-grade oil, 100 barrels of medium-grade oil, and 200 barrels of low-grade oil and costs $10,000 to operate. The company must produce at least 800 barrels of high-grade oil, 900 barrels of medium-grade oil, and 1,000 barrels of low-grade oil. What is the minimum cost to operate both refineries? Do not include a comma in your answer.
A mining company owns two mines. These mines produce an ore that can be graded into two classes: regular grade and low grade. The company must produce at least 410 tons of regular-grade and 530 tons of low-grade ore per week. The first mine produces 6 tons of regular-grade and 16 tons of low-grade ore per hour. The second mine produces 20 tons of regular-grade and 10 tons of low-grade ore per hour. The operating cost of the first mine is $9000 per hour, and the operating cost of the second mine is $30,500 per hour. The first mine can be operated no more than 55 hours a week, and the second mine can be operated no more than 29 hours a week. How many hours per week should each mine be operated to minimize the cost? First Mine: __ hours Second Mine:__ hours
Blue Ridge Hot Tubs manufactures and sells two models of hot tubs: the Aqua-Spa and the Hydro-Lux. Howie Jones, the owner and manager of the company, needs to decide how many of each type of hot tub to produce during his next production cycle. Howie buys prefabricated fiberglass hot tub shells from a local supplier and adds the pump and tubing to the shells to create his hot tubs. (This supplier has the capacity to deliver as many hot tub shells as Howie needs.) Howie installs the same type of pump into both hot tubs. He will have only 200 pumps available during his next production cycle. From a manufacturing standpoint, the main difference between the two models of hot tubs is the amount of tubing and labor required. Each Aqua-Spa requires 9 hours of labor and 12 feet of tubing. Each Hydro-Lux requires 6 hours of labor and 16 feet of tubing. Howie expects to have 1,566 production labor hours and 2,880 feet of tubing available during the next production cycle. Howie earns a profit of…
A company manufactures paring knives and pocket knives. Each paring knife requires 3 labor-hours, 7 units of steel, and 4 units of wood. Each pocket knife requires 6 labor-hours, 5 units of steel, and 3 units of wood. The profit on each paring knife is $3, and the profit on each pocket knife is $5. Each day the company has available 102 labor-hours, 157 units of steel, and 123 units of wood. Suppose that the number of labor-hours that are available each day is increased by h. For what values of h will a change of h labor-hours not change the shadow price of labor? The shadow price of labor will not change for shs. (Simplify your answers.)
A patient takes vitamin pills. Each day he must have at least 540 IU of vitamin A, 24 mg of vitamin B,, and 70 mg of vitamin C. He can choose between pill 1, which contains 240 IU of vitamin A, 4 mg of vitamin B,, and 10 mg of vitamin C, and pill 2, which contains 60 IU of vitamin A, 4 mg of vitamin B,, and 20 mg of vitamin C. Pill 1 costs 10¢, and pill 2 costs 30¢. Complete parts a and b below. a. How many of each pill should he buy in order to minimize his cost? What is the minimum cost? He should buy of pill 1 and of pill 2. The minimum cost is $ (Simplify your answers. Type integers or decimals.)
You are in charge of purchases at the student-run used-book supply program at your college, and you must decide how many introductory calculus, history, and marketing texts should be purchased from students for resale. Due to budget limitations, you cannot purchase more than 1050 of these textbooks each semester. There are also shelf-space limitations: Calculus texts occupy 2 units of shelf space each, history books 1 unit each, and marketing texts 5 units each, and you can spare at most 1,900 units of shelf space for the texts. If the used book program makes a profit of $10 on each calculus text, $4 on each history text, and $8 on each marketing text, how many of each type of text should you purchase to maximize profit? HINT [See Example 3.] calculus text(s) history text(s) marketing text(s) What is the maximum profit the program can make in a semester?
Trans Global Tractor Trailers has decided to spend up to $2,700,000 on a fleet of new trucks, and it is considering three models: the Gigahaul, which has a capacity of 6,000 cubic feet and is priced at $60,000; the Megahaul, with a capacity of 5,000 cubic feet, priced at $50,000; and the Picohaul, with a capacity of 2,000 cubic feet, priced at $40,000. The anticipated annual revenues are $500,000 for each new truck purchased (regardless of size). Trans Global would like a total capacity of up to 234,000 cubic feet and feels that it cannot provide drivers and maintenance for more than 54 trucks.How many of each should it purchase to maximize annual revenue? (Gigahaul, Megahaul, Picohaul) = trucks What is the largest possible revenue it can make? $
A zookeeper has a walrus with a nutritional deficiency. She wants to make sure the walrus consumes at least 2700 mg of iron, 2400 mg of vitamin B-1, and 1800 mg of vitamin B-2, One Maxivite pill contains 500 mg of iron, 200 mg of vitamin B-1, and 100 mg of vitamin B-2, and costs $0.05. One Healthovite pill provides 100 mg of iron, 150 mg of vitamin B-1, and 150 mg of vitamin B-2, and costs $0.06. Complete parts (a)-(c) below. (a) What combination of Maxivite and Healthovite pills will meet the walrus's requirement at lowest cost? What is the lowest cost? Set up the linear programming problem. Let m represent the number of Maxivite pils, h represent the number of Healthovite pills, and c represent the total cost in dollars. Minimize c= 0.05m + 0.06h subject to 500m + 100h 2 2700 200m + 150h 2 2400 100m + 150h 2 1800 m20, h 2 0. (Use integers or decimals for any numbers in the expressions. Do not include the $ symbol in your answers.) The best combination of pilts that moets the walrus's…

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