Question #13533

A biscuit factory has daily fixed costs of RM500. In addition, it costs 80 cents to produce each bag of biscuits. A bag of biscuits sells for RM 1.80. Given that x represents the number of bag of biscuits,
(a) Find
(i) Cost function, C(x)
(ii) Revenue function, R(x)
(iii) Profit function, P(x)
(b) Calculate the daily profit if the factory sells 1200 bags of biscuits daily.

Expert's answer

(a)(i) Cost function, C(x)

Linear Manufacturing Cost Function = Fixed Cost + (Average Variable Cost) * Output

C(x) = Fixed Cost + (Average Variable Cost) * Output

DAILY fixed costs = RM500

C(x) = RM500 + (Average Variable Cost) * Output

VARIABLE costs: 80 cents to produce each bag of biscuits

C(x) = RM500 + (80 cents) * Output

x represents the number of bags of biscuits sold (we will assume the number of bags sold is equal to the number of bags manufactured)

C(x) = RM500 + (80 cents) * x

>>> Daily Cost Function: C(x) = 500 + (.80) * x

(a)(ii) Revenue function, R(x)

The DAILY revenue is the selling price of a bag of biscuits multiplied by the number of bags sold that day.

R(x) = (Selling Price) * (bags sold)

A bag of biscuits sells for RM 1.80

R(x) = (1.80) * (bags sold)

(we will again assume the number of bags sold is equal to the number of bags manufactured)

R(x) = (1.80) * x

>>> Revenue Function: R(x) = (1.80) * x

(a)(iii) Profit function, P(x)

The profit is the difference between revenue received and cost of manufacturing.

P(x) = Revenue - Cost

P(x) = R(x) - C(x)

P(x) = (1.80) * x - [500 + (.80) * x]

P(x) = [(1.80) * x - (.80) * x] - 500

P(x) = [(1.80 - .80) * x] - 500

P(x) = [(1.00) * x] - 500

P(x) = (1.00)x - 500

P(x) = x – 500

>>> Daily Profit Function: P(x) = x - 500

(b) Calculate the daily profit if the factory sells 1200 bags of biscuits daily.

Daily Profit Function: P(x) = x - 500

P(x) = x - 500

P(x) = 1200 - 500

P(x) = 700

>>> Daily Profit: P(x) = RM 700

Linear Manufacturing Cost Function = Fixed Cost + (Average Variable Cost) * Output

C(x) = Fixed Cost + (Average Variable Cost) * Output

DAILY fixed costs = RM500

C(x) = RM500 + (Average Variable Cost) * Output

VARIABLE costs: 80 cents to produce each bag of biscuits

C(x) = RM500 + (80 cents) * Output

x represents the number of bags of biscuits sold (we will assume the number of bags sold is equal to the number of bags manufactured)

C(x) = RM500 + (80 cents) * x

>>> Daily Cost Function: C(x) = 500 + (.80) * x

(a)(ii) Revenue function, R(x)

The DAILY revenue is the selling price of a bag of biscuits multiplied by the number of bags sold that day.

R(x) = (Selling Price) * (bags sold)

A bag of biscuits sells for RM 1.80

R(x) = (1.80) * (bags sold)

(we will again assume the number of bags sold is equal to the number of bags manufactured)

R(x) = (1.80) * x

>>> Revenue Function: R(x) = (1.80) * x

(a)(iii) Profit function, P(x)

The profit is the difference between revenue received and cost of manufacturing.

P(x) = Revenue - Cost

P(x) = R(x) - C(x)

P(x) = (1.80) * x - [500 + (.80) * x]

P(x) = [(1.80) * x - (.80) * x] - 500

P(x) = [(1.80 - .80) * x] - 500

P(x) = [(1.00) * x] - 500

P(x) = (1.00)x - 500

P(x) = x – 500

>>> Daily Profit Function: P(x) = x - 500

(b) Calculate the daily profit if the factory sells 1200 bags of biscuits daily.

Daily Profit Function: P(x) = x - 500

P(x) = x - 500

P(x) = 1200 - 500

P(x) = 700

>>> Daily Profit: P(x) = RM 700

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