Question

A company has fixed monthly costs of $130,000 and production costs on its product of $32 per unit. The company sells its product for $66 per unit. The cost function, revenue function and profit function for this situation are a) C(x) = 32x+ 130000 ; R(x) = 66x; P(x) = 34x+ 130000b) C(x) = 66x+ 10858 ; R(x) = x+ 13 ; P(x) = − 34x+ 130000c) C(x) = 32x+ 130000 ; R(x) = 66x; P(x) = 34x− 130000d) C(x) = 66x; R(x) = 32x+ 130000 ; P(x) = − 34x+ 130000e) C(x) = 32x− 130000 ; R(x) = 66x; P(x) = 34x− 130000f) None of the above.

Answer 1

Answer:

  c)  C(x) = 32x+ 130000 ; R(x) = 66x; P(x) = 34x− 130000

Step-by-step explanation:

If x is the number of units, and if each unit costs $32 to produce, the cost function must include the term 32x. If additional fixed costs are 130000, the cost function must show that added to the per-unit costs:

  C(x) = 32x +130000 . . . . . matches choices (a) and (c) only

These answer choices agree that the revenue function is ...

  R(x) = 66x

Of course, the profit function is their difference:

  P(x) = R(x) -C(x) = 66x -(32x +130000)

Since the minus sign gets distributed to both terms inside parentheses, the profit function simplifies to ...

  P(x) = 34x -130000 . . . . . matches choice (c)

Answer 2

Answer:

Step-by-step explanation:

Revenue is expressed as total cost + profit

R = P + C

Let x represent the number of units produced and sold.

The company has fixed monthly costs of $130,000 and the production costs of its product is $32 per unit. This means that total cost of producing x units will be

2000 + 32x

The company sells its product for $66 per unit. The total revenue from selling x units would be

66×x = $66x

Therefore,

The cost function is

C(x) = 32x + 2000

The Revenue function is

R(x) = 66x

The profit function would be R(x) - C(x). It becomes

P(x) = 66x - 32x - 2000

P(x) = 34x - 2000