1. In business, functions that involve Revenue, Cost, and Profit are used. Suppo

Question

1. In business, functions that involve Revenue, Cost, and Profit are used. Suppose R(x), C(X), and P(X), denote the total revenue, cost, and profit functions respectively. Given that the Profit Equation, P(x) = R(x) - C(x), find P(100) (Points : 2) 2. A company manufacturing radios has an average cost function given by: , where x is the number of radios produced. What does the Average Cost tend to as production increases? (Points : 2) 3. The demand equation for a certain item is p = 14 - (x/1,000) and the cost equation is C(x) = 7,000 + 4x. Find the marginal profit at a production level of 3,000 and interpret the result. (Points : 2)

Explanation / Answer

R = -0.2x^2 + 40x + 200

C = 500 + 3x

P = R - C

P = -0.2x^2 + 40x + 200 - (500 + 3x)

P = -0.2x^2 + 37x - 300

P(100) = -0.2(100)^2 + 37(100) - 300

P(100) = 1400 ----> ANSWER

-------------------------------------------------------------------------

2)

Cbar = average cost = 175 + 205/x

When x increases, as in when x ---> infinity, the term 205/x = 205/infinity tends to 0

So, Cbar tends to : Cbar = 175 + 0 = 175

So, 175 ----> ANSWER

---------------------------------------------------------------------------------

3)

p = 14 - x/1000

C = 7000 + 4x

Revenue = p*x = x(14 - x/1000) = -x^2/1000 + 14x

Profit, P = R - C

P = -x^2/1000 + 14x - (7000 + 4x)

P = -x^2/1000 + 10x - 7000

P' = -x/500 + 10

Now, plug in x = 3000 :

P' = -3000/500 + 10

P' = -6 + 10

P' = 4

So, answer option 4

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.