Question

To produce x units of a religious medal costs C(x) = 16x +48. The revenue is R(x) = 32x. Both cost and revenue are in dollars.a. Find the break-even quantity.b. Find the profit from 310 units.c. Find the number of units that must be produced for a profit of $160.a. 3 units is the break-even quantity. b. The profit for 310 units is $___

Answer 1

Answer:

a) the break-even quantity is 3 units

b) The profit for 310 units is $4912

c) To get a profit of $160, 13 units must be produced

Step-by-step explanation:

Given:

cost function: C(x) = 16x +48

revenue function: R(x) = 32x

To find:

a. Find the break-even quantity.

b. Find the profit from 310 units.

c. Find the number of units that must be produced for a profit of $160

a) Break-even quantity is gotten when the cost function = revenue function

C(x) = R(x)

16x + 48 = 32x

48 = 32x - 16x

48 = 16x

x = 48/16

x = 3

Hence, the break-even quantity is 3 units

b) Profit = Revenue - cost

Profit = R(x) - C(x)

Profit = 32x - (16x + 48)

Profit = 32x - 16x - 48

Profit = 16x - 48

if number of units = 310, x = 310

Profit = 16(310) - 48

Profit = $4912

The profit for 310 units is $4912

c) when profit = $160, x = ?

Profit = 16x - 48

160 = 16x - 48

160 + 48 = 16x

208 = 16x

x = 208/16

x = 13

To get a profit of $160, 13 units must be produced