Question

2. The cost of producing x units of a certain commodity is given by P
x
1000

0
x
MC
sds,
where P is in dollars and M
x is marginal cost in dollars per unit.
A. Suppose the marginal cost at a production level of 500 units is $10 per unit, and the cost
of producing 500 units is $12, 000 (that is, M
500
10 and P
500
12000).
Use a tangent line approximation to estimate the cost of producing only 497 units.

B. Suppose the production schedule is such that the company produces five units each day.
That is, the number of units produced is x
5t, where t is in days, and t
0 corresponds to
the beginning of production. Write an equation for the cost of production P as a function of
time t.
C. Use your equation for P
t from part B to find dP
dt . Be sure to indicate units and describe
what dP
dt represents, practically speaking.

Answer 1

I got A can someone help me with C and B please?

Answer 2

What does the question mark within a black square represent? Hard to know what you are asking.
Online, “*” is used to indicate multiplication to avoid confusion with “x” as an unknown.
Online "^" is used to indicate an exponent, e.g., x^2 = x squared.