Problem 1 If company A manufactures t-shirts and sells them to retailers for US$9.80 each.It has fixed costs of $2625 related to the production of the t-shirts, and the production cost per unit is US$2.30. Company B also manufactures t-shirts and selll them directly to consumers.The demand for its product is p = 15 − x/125 , its production cost per unit is US$5.00and its fixed cost are the same as for company A .Derive the total revenue function, R(x) for company A.Derive the total cost function, C(x) for company A.Derive the profit function, Π(x) for company A. Using a spreadsheet, create a table for showing x, R(x) , C(x) for company A in the domain x = 50, 100, 150, 200, 250, 300, 350, 400, 450. Graph the functions from (d) above on the same axes.From your graph, determine the break-even level of output for company A. Derive the total revenue function, R(x) for company B.Derive the profit function, Π(x) for company B.How many t-shirts must company B sell to in order to break-even.How many t-shirts must company B sell to maximise its profit. Problem 2 (a) A company has determined that its profit for a product can be described by a linear function. The profit from the production and sale of 150 units is $455, and the profit from250 units is $895. What is the average rate of change of the profit for this product when between 150 and 250 units are sold? Write the equation of the profit function for this product. How many units give break-even for this product? (b) You are the CEO for a lightweight compasses manufacturer. The demand function for the lightweight compasses is given by p = 40 − 4q2where q is the number of lightweight compasses produced in millions. It costs the company $15 to make a lightweight compass. Write an equation giving profit as a function of the number of lightweight compasses produced. At the moment the company produces 2 million lightweight compasses and makes a profit of $18,000,000, but you would like to reduce production. What smaller number of lightweight compasses could the company produce to yield the same profit?

Since multiple questions are posted only the first question will be answered and this question has…

Answered: f company A manufactures t-shirts and…

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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Problem 1

If company A manufactures t-shirts and sells them to retailers for US$9.80 each.

It has fixed costs of $2625 related to the production of the t-shirts, and the production cost per unit is US$2.30. Company B also manufactures t-shirts and selll them directly to consumers.

The demand for its product is p = 15 − ^x/₁₂₅ , its production cost per unit is US$5.00

and its fixed cost are the same as for company A .

Derive the total revenue function, R(x) for company A.
Derive the total cost function, C(x) for company A.
Derive the profit function, Π(x) for company A.

Using a spreadsheet, create a table for showing x, R(x) , C(x) for company A in the domain x = 50, 100, 150, 200, 250, 300, 350, 400, 450.

Graph the functions from (d) above on the same axes.
From your graph, determine the break-even level of output for company A.

Derive the total revenue function, R(x) for company B.
Derive the profit function, Π(x) for company B.
How many t-shirts must company B sell to in order to break-even.
How many t-shirts must company B sell to maximise its profit.

Problem 2

(a) A company has determined that its profit for a product can be described by a linear function. The profit from the production and sale of 150 units is $455, and the profit from

250 units is $895.

What is the average rate of change of the profit for this product when between 150 and 250 units are sold?

Write the equation of the profit function for this product.

How many units give break-even for this product?

(b) You are the CEO for a lightweight compasses manufacturer. The demand function for the lightweight compasses is given by p = 40 − 4q²where q

is the number of lightweight compasses produced in millions. It costs the company $15 to make a lightweight compass.

Write an equation giving profit as a function of the number of lightweight compasses produced.

At the moment the company produces 2 million lightweight compasses and makes a profit of $18,000,000, but you would like to reduce production. What smaller number of lightweight compasses could the company produce to yield the same profit?

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