A manufacturing company has a total cost functions
c =5Q+ 180Q +12500
This gives the total cost of producing Q untis
a) find a formula for the units cost U in terms of Q where U = C/Q
b)find the value Q that minimises the unit cost find this minimum unit cost.
b)find the value Q that minimises the unit cost find this minimum unit cost.
b) b)find the value Q that minimises the unit cost find this minimum unit cost.
why post this three times?
What have you done so far?
Assuming you meant C=5Q^2+ 180Q +12500
(a) U=C/Q = 5Q+ 180 +12500/Q
(b) dU/dQ = 5 - 12500/Q
minimum is U(50) = 680
To find the formula for the unit cost, U, in terms of Q, we need to divide the total cost function, C, by the quantity of units, Q.
a) Formula for Unit Cost (U):
The total cost function is given as:
C = 5Q + 180Q + 12500
To find the unit cost, U = C/Q, we substitute the total cost function into the unit cost formula:
U = (5Q + 180Q + 12500) / Q
Simplifying this expression, we get:
U = (185Q + 12500) / Q
So, the formula for the unit cost, U, in terms of Q is U = (185Q + 12500) / Q.
b) Finding the value of Q that minimizes the unit cost and the minimum unit cost:
To find the value of Q that minimizes the unit cost, we need to differentiate the unit cost function, U, with respect to Q and set it equal to zero. In other words, we find the value of Q at which the derivative of U with respect to Q is zero.
Differentiating the unit cost function, U, with respect to Q:
dU/dQ = (d/dQ)(185Q + 12500) / Q
Using the quotient rule for differentiation, we get:
dU/dQ = (185Q - (185Q + 12500)) / Q^2
= -12500 / Q^2
Setting the derivative equal to zero:
-12500 / Q^2 = 0
Solving for Q, we find that Q = ∞ (which implies no production, so it does not make sense in this context).
Therefore, as the derivative does not exist at Q = ∞, there is no minimum unit cost.