A company produces a product which it sells for $55 per unit. Each unit costs the firm $23 in variable expenses, and fixed costs on an annual basis are $400,000. If x equals the number of units produced and sold during the year:
a) Formulate the linear total cost function
b) Formulate the linear total revenue function
c) Formulate the linear profit function
d) What does annual profit equal if 10,000 units are produced and sold during the year?
e) What level of output is required in order to earn zero profit?
Answers
Step-by-step explanation:
GiveN:-
A father is 7 times as old as his son, two years ago the Father was 13 times as old as his son.
To FinD:-
The present age of son.
SolutioN:-
Let the present age of the son be x years.
Let the present age of the father be 7x years.
2 years ago their ages were:-
Son = (x - 2) years.
Father = (7x - 2) years.
It is said that two years ago the Father was 13 times as old as his son.
According to the question,
\large\implies{\sf{7x-2=13(x-2)}}⟹7x−2=13(x−2)
\large\implies{\sf{7x-2=13x-26}}⟹7x−2=13x−26
\large\implies{\sf{-2+26=13x-7x}}⟹−2+26=13x−7x
\large\implies{\sf{24=6x}}⟹24=6x
\large\implies{\sf{\dfrac{24}{6}=x}}⟹
6
24
=x
\large\implies{\sf{\dfrac{\cancel{24}}{\cancel{6}}=x}}⟹
6
24
=x
\large\implies{\sf{4=x}}⟹4=x
\large\therefore\boxed{\bf{x=4.}}∴
x=4.
Their present ages:-
Son's age = x = 4 years.
Father's age = 7x = 7 × 4 = 28 years.
The present age of the son is 4 years.