A monopolistic producer of two goods has a total cost function TC = 5Q1+ 10Q2 and a totalrevenue TR = 50Q1- Q1² – 2Q2Q1+100Q2– 4Q22Using the same functions as given in Question 1, now consider when the firm's total costs arefixed at RM200.i) Calculate the values of Q, and Q2 will yield a maximum profit using Lagrange MultiplierMethod.

By Method of lagranges multiplier . To maximize f(x,y,z) subject to g(x,y,z)=k Solve system of…

Answered: A monopolistic producer of two goods…

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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5) Given P=5900-10Q, Costs that will not change due to production is $845 and Cost that depends on use of Electricity, gas, Raw materials, Labour, etc. is given by the function 2Q^3 - 4Q^2 +140Q.Find optimal output, price and maximum profit and verify using second order conditions.
A firm has identified that total profit P as a function of the number of units of two products manufacturedis given by the following functionP = 12x1 + 32x2 – 2x12– 8x22– 1000where x1 = thousands of units of Product 1 and x2 = thousands of units of Product 2. The number of units ofeach product that can be produced in the next planning period is constrained by the fact that there are only12,000 pound of an ingredient that is used in the production of both products available. Both products requiretwo pounds of the ingredient per unit produced.i) Formulate a mathematical model that can be used to determine how much of each product should bemanufactured in the next planning period so as to maximise profit.ii) Find a solution to your mathematical model.
Q1) A retail. Store stocks two types of shirts A and B. These are packed in attractive cardboard boxes. During a week the store can sell a maximum of 400 shirts of type A and a maximum of 300 shirts of type B. The storage capacity, however, is limited to a maximum of 600 of both types combined. Type A shirt fetches a profit of SR 2/- per unit and type B a profit of SR. 5/- per unit. (a) Formulate a mathematical model of the problem.
Two numbers are greater than 10 but less than 40. Their GCF is 17. What are the two numbers?
2. Consider the function y(x) = 5x over the interval [0, 10]. (a) If the points A(0, y(0)), B(5, y(5)), and C(10, y(10)) are on the curve represented by the above function, find the slope of the lines (secants) AB, and AC, respectively. (b) If x represents time and y represents the displacement of a particle moving along a line, what is the physical meaning of your results to part (a)? (c) Now consider a point D(10 – h, y(10 – h)) on the curve represented by the given function, find the slope of the line DC. (d) As h → 0, what is the limiting value of your result to part (c)? (e) What is its physical meaning of your result to part (d) if again x represents time and y represents the displacement?
Suppose that the demand equation and the cost function are given by –p = 125 − 0.1q C(q) = 800 + 12q + 0.02q2 Find the quantity q that maximizes the profit. What is the maximumprofit?
The hourly cost function (in dollars) of 3 generators, each as follows: where x₁ is the output power of the first generator, x₂ is the output power of the second generator, and x3, is the output power of the third generator. It is known that the three generators serve a load (total output power) of 744 megawatts. Determine the distribution of power that must be generated by each generator so that it can meet the needs load with minimum total operating costs.

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