Task 1A company faces randomly fluctuating demand on the sales market. Let thelevel of demand X be distributed as follows:f(r) =1för 0

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Answered: A company faces randomly fluctuating…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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In the manufacture of a product, fixed costs per week are $4000. Fixed costs are costs, such as rent and insurance, that remain constant at all levels of production during a given time. If the marginal-cost dc function is dq 0.000001q? – 0.25q + 0.2. (i) Compute the fixed cost of producing 10,000 kg in l week. (ii) Compute the total cost of producing 10,000 kg in 1 week.
15(b). The demand function for a manufacturer's product is p = 12- 0.03q where p is the price per unit and q is the number of units. Find the manufacturer's expected maximum revenue.
The following figure shows how the concentration of ingested microplastic pieces (number of pieces per fish) depends on the body length in the Round Goby fish. 60 (b) r^2=0.3934 P= 0.0097 Concentration (No. Fish¹) ON WA 40 50 30 20-A 10 Δ 5 6
2. A simple curve that often makes a good model for the variable costs of a company, as a function of the number of units produced, x, has the form: y = b₁x + b₂x² + b3x³. (There is no constant term because fixed costs are not included.) Consider the following table of recorded variable costs versus units produced for some company:
VI. Determine all the relative minimum and maximum values, and saddle points of the function h defined by h(x, y) = x³ –y + 3ry². -3%
Q. 1. Use production function q(L, K) = L3 K and derive the followings: (a) (b) (c) (d) Short-run and long-run profit functions Short-run and long-run cost functions Short-run and long-run supply function using Hotelling's lemma. Short-run and long-run supply function using Shephard's lemma.
A model is built to explain the evolution of spending on tourism and recreation in a certain group of families (Y in USD/person/year). As potential explanatory variables are considered: X1 average annual income per person in the family (in USD), X2 – number of people in the family, X3 – nature of employment of the head of household If X3=1, when the head of the family is self-employed, X3=0, when the head of the family is an employee Based on the collected data, linear correlation coefficients between variables were calculated and obtained 0,84 R, = -0,47 [1 -0,55 0, 62 R= 1 -0,42 0,75 1 Using Hellwig's method, select the optimal combination of explanatory variables for the tourism and recreation expenditure model.
10.23. Question. An umbrella-shaped island has a population of 499 healthy people. Alice, who is injected with the T-virus, enters the island on day 0. It is known that anyone infected with the T-virus will become a zombie after 24 hours. Assume that the infected (zombies are considered infected) will spread the virus (through biting) and no one on this island can escape from it. The rate of virus transmission is proportional to the product of the number of infected and non-infected. Thus, if x(t) denotes the number of the infected on day t, then dx dt = kx(500 — x). On day 10, it is observed that 20 people are already infected. Answer the following questions. (a) How many zombies are on the island on day 16? (b) On day 20, how many people are infected but not yet turned into a zombie? (c) A rescue boat with 50 available seats is to be sent to the island. What is the earliest day the boat should be sent to ensure it can rescue all survivors (those not infected)?
A toll bridge charges $1.00 for passenger cars and $2.75 for other vehicles. Suppose that during daytime hours, 65% of all vehicles are passenger cars. If 20 vehicles cross the bridge during a particular daytime period, what is the resulting expected toll revenue? [Hint: Let X = the number of passenger cars; then the toll revenue h(X) is a linear function of X.]
(d) Suppose that new copies cost $150 and used copies cost $80. Assume the bookstore currently has 50 new copies and 50 used copies. What is the expected value of total revenue from the sale of the next 15 copies purchased? [Hint: Let h(X) = the revenue when X of the 15 purchasers want new copies. Express this as a linear function.] $

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A company faces randomly fluctuating demand on the sales market. Let the level of demand X be distributed as follows: f(r) = for 0