A simple economy consists of two industries: agriculture and manufacturing. The production of 1 unit of agricultural products requires the consumption of 0.2 unit of agricultural products and 0.3unit of manufactured goods. The production of 1 unit of manufactured goods requires the consumption of 0.4 unit of agricultural products and 0.3 unit of manufactured goods.(a) Find the total output of goods needed to satisfy a consumer demand for $100 million worth of agricultural products and $130 million worth of manufactured goods. (Round youranswers to one decimal place.)agricultural productsmanufactured goods$millionmillion(b) Find the value of the goods consumed in the internal process of production in order to meet the gross output. (Round your answers to one decimal place.)agricultural productsmillionmillionmanufactured goodsNeed Help? Read ItWatch It

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Answered: A simple economy consists of two…

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 manufacturer of Bluetooth headphones examines the historical demand of its product and learns that the average monthly demand is about 3,090 headphones but varies between 2,350 and 4,100 headphones. Each pair of the headphones has a retail price of $120. The monthly fixed production cost ranges from $5,500 to $6,500, with an average of $6,000. The average variable cost of producing a pair of headphones is $35, but because the manufacturing process is not fully automated, the variable cost may vary between $31 and $39 per pair. Develop a risk analysis model to answer the following questions. What is the monthly profit from the Bluetooth headphones for the most likely, pessimistic, and optimistic scenarios? The company notices that during the holiday season in December, the demand tends to be higher than in other months. Historically, the demand in December is about 3,578 pairs on average, but also ranges from 2,535 to 4,757 pairs. What is the December profit for the most…
Consider a manufacturing firm that has revenues of $160 per day. The firm must transport its output to a central freight terminal. Transportation costs to get output to the central freight terminal are $20 The firm employs labour that costs $60 per day if employed at the central freight terminal location, but those daily labour costs fall at a rate of $4 per mile from center. The firm has other non-land costs of $30 per day to buy raw materials.The firm requires 2 hectares of land for its operations. a) What is the firm's maximum willingness to pay per hectare of land at the central freight terminal location? Show your work. b) What is the equation of the firm's bid rent for land per hectare as a function of x, where x is distance in miles from the central freight terminal? Show your work. per mile.
Solve the problem. Suppose an economy consists of three sectors: Energy (E), Manufacturing (M), and Agriculture (A). Sector E sells 70% of its output to M and 30% to A. Sector M sells 30% of its output to E, 50% to A, and retains the rest. Sector A sells 15% of its output to E, 30% to M, and retains the rest. Denote the prices (dollar values) of the total annual outputs of the Energy, Manufacturing, and Agriculture sectors by Pe. Pm, and Pa respectively. If possible, find equilibrium prices that make each sector's income match its expenditures. Find the general solution as a vector, with pa free. 0.356 Pal Pm-0.686 Pa Pe Pa Pe Pm Pa Pe Pm - Pa Pe Pm Pa Pa [0.465 Pa = 0.593 Pa Pa [0.308 Pa 0.716 Pa Pa 0.607 Pa 0.481 Pa Pa
A produce grower is purchasing fertilizer containing 3 nutrients: A, B and C. The minimum weekly requirements are 80 units of A, 120 of B and 240 of C. There are two popular blends of fertilizer on the market. Blend 1 costing $8 a bag and contains 2 units of A, 6 of B and 4 of C. Blend 2 costing $10 a bag and contains 2 units of A, 2 of B and 12 of C. (a) Write down the LP Model. (b) Identify the coordinates of the extreme points of the feasible region. (c) How many bags of each blend should the grower buy each week to minimize the cost of meeting the nutrient requirement. (d) What is the mimimim cost ?
Chemco produces two chemicals: A and B. Thesechemicals are produced via two manufacturing processes.Process 1 requires 2 hours of labor and 1 lb of raw materialto produce 2 oz of A and 1 oz of B. Process 2 requires 3hours of labor and 2 lb of raw material to produce 3 oz ofA and 2 oz of B. Sixty hours of labor and 40 lb of rawmaterial are available. Demand for A is unlimited, but only20 oz of B can be sold. A sells for $16/oz, and B sells for$14/oz. Any B that is unsold must be disposed of at a costof $2/oz. Formulate an LP to maximize Chemco’s revenueless disposal costs.
A brewery produces regular beer and a lower-carbohydrate "'light" beer. Steady customers of the brewery buy 12 units of regular beer and 18 units of light beer monthly. While setting up the brewery to produce the beers, the management decides to produce extra beer, beyond that needed to satisfy customers. The cost per unit of regular beer is $32,000 and the cost per unit of light beer is $60,000. Every unit of regular beer brings in $100,000 in revenue, while every unit of light beer brings in $300,000 in revenue. The brewery needs at least $9,000,000 in revenue, and has determined that the total demand will be at least 50 units of beer. Complete parts (a) and (b). (a) How much of each type of beer should be made so as to minimize total production costs? ◻️units of regular beer and◻️ units of light beer should be made, for a minimum total cost of $◻️
A certain company is producing and selling its product X. The variable cost of the product X is 60% of its selling price, and the fixed cost of the company is $50,000 per month. When the company’s target profit for the forthcoming month is $20,000, how much sales volume (in dollars) is required to meet it?
The monthly demand for Williams Tchotchkes (q measured in 1000s of tchotchkes) depends on the price that they set for their tchotchkes (p measured in dollars), the average price of substitutes for their tchotchkes (p, also measured in dollars), and the average monthly disposable income in the market for tchotchkes (y measured in $1000s). The current prices are p = $10 and p₁ = $11, the current monthly demand for Williams Tchotchkes is 8000 tchotchkes and the current average monthly disposable income in the tchotchkes market is $3500. Furthermore, it is known that Əq Op p=10 Pg=11 y=3.5 = -0.31, Əq aps P=10 Pg=11 y=3.5 = 0.44 and Əq dy p=10 Pg=11 y=3.5 = 0.72. Scenario 1: Suppose that p increases by $0.20, p, increases by $0.35 (from their current values), and income doesn't change. In this scenario, monthly demand for Williams Tchotchkes' monthly will [Select] , and Williams Tchotchkes' monthly revenue will [Select] Scenario 2: Now (instead) suppose that average monthly income in the…
Succulent Citrus produces orange juice and orange concentrate. This year the company anticipates a demand of at least 12,000 quarts of orange juice and 1,500 quarts of orange concentrate. Each quart of orange juice requires 10 oranges, and each quart of concentrate requires 50 oranges. The company also anticipates using at least 270,000 oranges for these products. Each quart of orange juice costs the company 50¢ to produce, and each quart of concentrate costs $2.00 to produce. How many quarts of each product should Succulent Citrus produce to meet the demand and minimize total costs? orange juice qt qt orange concentrate
An agricultural company markets two types of food compounds for animals. The first contains 4 units of nutrient A and 2 units of nutrient B, the second contains 2 units of the prime nutrient A and 3 units of the nutrient prima B. You want to achieve a diet that provides at least 20 units of A and 18 units of B. If the cost of one unit of the first compound is $2 USD and the second is $2.5 USD, calculate how much of each type of compound must be taken for a minimum cost.
A florist provides fresh flowers to shops in Wollongong. At present she has one nursery in Goulburn with capacity 9000 units a year. The florist is considering opening shops in Canberra and Sydney, and has found three potential nursery sites at Wagga, Orange and Bathurst. The transportation tableau below summarises the projected nursery capacities (units), the cost per unit of shipping from each nursery to each destination (dollars), and the demand (units) for the coming year. j=1 j=2 j=3 Sydney Capacities Wollongong Canberral 5 i=1 Goulburn 12 9000 i=2 Wagga 7 10 4000 i=3 Orange 4 7000 i=4 Bathurst 11000 Demand 11000 5000 8000 There are further constraints on how the nurseries can be located: • If a nursery is located in Wagga, another must be located in Bathurst and vice- versa. • One nursery can be located in Orange or Bathurst, but not both. Suppose that the costs of establishing new nurseries are Wagga $180,000 Orange $160,000 Bathurst $270,000 The goal is to develop a 0-1…
A company is dedicated to the production of different vegetable-flavored milks. Currently the company produces two types of milk: almond and coconut, which it sells at $ 5,000 and $ 2,000 / liter respectively. Milk production is subject to the use of machine hours in the production plant and of water as a fundamental resource. It takes 1 machine-hour and 2 liters of water to produce 1 liter of almond milk, while it takes 3 machine-hours and 1 liter of water to produce 1 liter of coconut milk. The company currently has 100 machine-hours and 50 liters of water to make the milk, and it is also required to make at least 30 liters of milk in total. 1. Set up the linear programming model in standard format.2. Determine all the basic solutions to the problem. Identify which ones are feasible and which ones are not. Analyze what happens graphically.3. Determine an initial feasible basic solution using phase I. In each iteration, write the resulting model in dictionary format and analyze what…

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