Question

The formula below can be used to calculate

the annual profit that a company generates
from an item that it manufactures.
In one year Jonathan's company sold 7000
lamps, generating an annual profit of £12,330
The sale price of each lamp was £20 and
the annual fixed costs were £10,000.
Calculate the manufacturing cost of each
lamp.
P=N(S-C)-F
P is the annual profit (E)
I is the number of items sold
S is the sale price of each item (E)
C is the manufacturing cost of each item (E)
F is the annual fixed costs (E)

Answer 1

£16.81.

Explanation:

P = N(S - C) - F

Substituting the given values:

12330 = 7000(20 - C) - 10000

12330 = 140000 - 7000C - 10000

7000C = 140000 - 10000 - 12330

7000C = 117670

C = 117670/7000

= 16.81

Answer 2

£16.81

Explanation:

Given:

• P = £12,330
• N = 7,000
• S = £20
• F = £10,000

Substitute the given values into the formula and solve for C:

`\begin{aligned}P & =N(S-C)-F\\\implies 12330 &= 7000(20-C)-10000\\12330 &= 140000-7000C-10000\\12330+10000-140000 &=-7000C\\-117670 &=-7000C\\7000C &=117670\\C & =(117670)/(7000)\\C & =16.81\end{aligned}`