Answered

Discover a wealth of knowledge at Westonci.ca, where experts provide answers to your most pressing questions. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

4) A company manufactures widgets. The expense function E=8q+12,000 and the
demand function q= -10p +20,000, where p is the price.

a. Express the variable expense V in terms of q, where q is the quantity of widgets
produced

b. Express the total expenso E in terms of p.

c. Determine the Revenue R in terms of p. (Hint: R=p•q).

d. Determine the profit P in terms of p. (Hint: P=R-E).

e. Determine the price that will yield the maximum profit. (Hint: x = -b/2a).

f. Determine the maximum profit.

Sagot :

MrRoyal

Revenue, profit and expenses are all integral parts of a company's balance sheet

  • The expense in terms of q is [tex]\mathbf{E = 8q + 12000}[/tex]
  • The expense in terms of p is [tex]\mathbf{E = -80p + 172000}[/tex]
  • The revenue in terms of p is [tex]\mathbf{R = -10p^2 + 20000p}[/tex]
  • The profit in terms of p [tex]\mathbf{P =-10p^2 + 20080p - 172000}[/tex]
  • The price that yields the maximum profit is $1004
  • The maximum profit is $9908160

The expense function is given as:

[tex]\mathbf{E = 8q + 12000}[/tex]

The demand function is given as:

[tex]\mathbf{p = -10p + 20000}[/tex]

(a) The expense in terms of q

This is already given as: [tex]\mathbf{E = 8q + 12000}[/tex]

(b) The expense in terms of p

Substitute -10p + 20000 for p in [tex]\mathbf{E = 8q + 12000}[/tex]

[tex]\mathbf{E = 8(-10p + 20000) + 12000}[/tex]

Expand

[tex]\mathbf{E = -80p + 160000 + 12000}[/tex]

[tex]\mathbf{E = -80p + 172000}[/tex]

(c) The revenue in terms of P

This is calculated as:

[tex]\mathbf{R = p \times q}[/tex]

So, we have:

[tex]\mathbf{R = p \times (-10p + 20000)}[/tex]

Expand

[tex]\mathbf{R = -10p^2 + 20000p}[/tex]

(d) The profit in terms of p

We have:

[tex]\mathbf{R = -10p^2 + 20000p}[/tex] and [tex]\mathbf{E = -80p + 172000}[/tex]

So, the profit P is calculated as:

[tex]\mathbf{P =R - E}[/tex]

This gives

[tex]\mathbf{P =-10p^2 + 20000p +80p - 172000}[/tex]

[tex]\mathbf{P =-10p^2 + 20080p - 172000}[/tex]

(e) The price that yields maximum profit

In (d), we have:

[tex]\mathbf{P =-10p^2 + 20080p - 172000}[/tex]

The maximum price is calculated using:

[tex]\mathbf{p = -\frac{b}{2a}}[/tex]

Where:

[tex]\mathbf{b =20080}[/tex]

[tex]\mathbf{a = -10}[/tex]

So, the equation becomes

[tex]\mathbf{p = -\frac{20080}{2 \times -10}}[/tex]

[tex]\mathbf{p = 1004}[/tex]

Hence, the price that yields the maximum profit is $1004

(f) The maximum profit

In (e), we have: [tex]\mathbf{p = 1004}[/tex]

Substitute 1004 for p in [tex]\mathbf{P =-10p^2 + 20080p - 172000}[/tex]

[tex]\mathbf{P =-10(1004)^2 + 20080(1004) - 172000}[/tex]

[tex]\mathbf{P =9908160}[/tex]

Hence, the maximum profit is $9908160

Read more about revenue, expenses and profit at:

https://brainly.com/question/23103804

We hope this was helpful. Please come back whenever you need more information or answers to your queries. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.