A factory, with fixed cost of £150, variable cost per unit of item is £2, and price function is p(x)=(30−0.2x)
.
Questions
You should answer the following questions and incorporate your answers into a word-processed report. The sections of your report should correspond to the individual questions below.
a)Find the total cost and revenue functions.
b)Find the breakeven point(s).
c)Plot the revenue and cost functions on graph, showing the break-even output
levels and corresponding price. (Label the graph properly)
d)Determine the profit function for the company and find,
(i)The level production that maximizes the profit.
(ii)The maximum profit.
Answers
Answer:
1 .26
2 .50
3 .6
4.6
next I don't know
please mark me as brainlist if correct answer
Given : A factory, with fixed cost of £150,
variable cost per unit of item is £2,
and price function is p(x)=(30−0.2x)
To find :
a)Find the total cost and revenue functions.
b)Find the breakeven point(s).
Solution:
Total cost = Fixed cost + variable cost
Fixed cost = £150
variable cost = 2x where x is number of units
C(x) = 150 + 2x £
price function is p(x)=(30−0.2x)
revenue = (30−0.2x)x
R(x) = 30x - 0.2x²
breakeven point
C(x) = R(x)
150 + 2x = 30x - 0.2x²
=> 0.2x² - 28x + 150 = 0
=> x² - 140x + 750 = 0
x ≈ 5.58 , 134.42
Hence break even point is after 6 units
Profit = R(x) - C(x)
= 30x - 0.2x² - 150 - 2x
= - 0.2x² + 28x - 150
dP/dx = -0.4x + 28
=> x= 70
d²P/dx² = - 0.4 < 0
Hence maximum profit at x = 70
Profit = - 0.2x² + 28x - 150
= - 0.2(70)² + 28(70)- 150
= 830
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