Allina opens an exotic bakery. Her capacity for the month is eight hundred (800) Love Cherry Short cakes. On average, in a month, she pays a fixed amount for water, electricity, security and a loan of TTD100.00, TTD1,200.00, TTD2,700.00 and TTD4,000.00 respectively. In addition, she estimates that TTD50.00 more must be paid for each Love Cherry Short cake she makes and sells. If she sells one Love Cherry Short cake for TTD90.00. Identify and clearly state all variables used. Determine the following:Allina’s total cost and revenue functions. From part a) state the domain and range the total cost and revenue functions. Allina’s total cost when she produces and sells one thousand Love Cherry Short cakes. the value of the rational function of total cost and total revenue when no Love Cherry Short cakes are made and sold.

Answered: pays a fixed amount for water,…

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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Question

Allina opens an exotic bakery. Her capacity for the month is eight hundred (800) Love Cherry Short cakes. On average, in a month, she pays a fixed amount for water, electricity, security and a loan of TTD100.00, TTD1,200.00, TTD2,700.00 and TTD4,000.00 respectively. In addition, she estimates that TTD50.00 more must be paid for each Love Cherry Short cake she makes and sells. If she sells one Love Cherry Short cake for TTD90.00. Identify and clearly state all variables used. Determine the following:
Allina’s total cost and revenue functions.
From part a) state the domain and range the total cost and revenue functions.

Allina’s total cost when she produces and sells one thousand Love Cherry Short cakes.
the value of the rational function of total cost and total revenue when no Love Cherry Short cakes are made and sold.

Expert Solution

Step 1: Notes and Question 1:

Since you have posted a multi subparts question according to guidelines I will solve first(1,2,3)three question for you. To get remaining part solved please repost the complete question and mention parts.

Variables:

Let C represent the total cost function.
Let R represent the total revenue function.
Let x represent the number of Love Cherry Short cakes produced and sold.
The fixed costs are as follows:
- Water cost (W) = TTD100.00
- Electricity cost (E) = TTD1,200.00
- Security cost (S) = TTD2,700.00
- Loan cost (L) = TTD4,000.00
Additional cost per cake produced (A) = TTD50.00
Selling price per cake (P) = TTD90.00

Now, let's answer each part of the question:

1. Allina's total cost and revenue functions:

The total cost function (C) can be expressed as: $C left parenthesis x right parenthesis space equals space W space plus space E space plus space S space plus space L space plus space A space cross times space x space C left parenthesis x right parenthesis space equals space 100 space plus space 1200 space plus space 2700 space plus space 4000 space plus space 50 space cross times space x space C left parenthesis x right parenthesis space equals space 8000 space plus space 50 x$
The total revenue function (R) is given by the selling price multiplied by the number of cakes sold: $R left parenthesis x right parenthesis space equals space P space cross times space x space R left parenthesis x right parenthesis space space space space space space space space space space equals space 90 space cross times space x$