A piano manufacturer has a daily fixed cost of $1200 and a marginal cost of $1500 per piano. Find the cost C(x) of manufacturing x pianos in onde day. Use your function to answer the following questions:
a)On a given day, what is the cost of manufacturing 3 pianos?
b)What is the cost of manufacturing the 3rd piano that day?
c)What is the cost of manufacturing the 11th piano that day?
A piano manufacturer has a daily fixed cost of $1,000 and a marginal cost of $1,300 per piano. Find the cost
C(x)
of manufacturing x pianos in one day.
What is the answer
To find the cost function C(x) of manufacturing x pianos in one day, we need to add the fixed cost and the marginal cost per piano.
a) The cost of manufacturing 3 pianos is given by:
C(3) = Fixed Cost + (Marginal Cost * Number of Pianos)
= $1200 + ($1500 * 3)
= $1200 + $4500
= $5700
Therefore, the cost of manufacturing 3 pianos is $5700.
b) The cost of manufacturing the 3rd piano that day can be found by evaluating C(3) and subtracting the cost of manufacturing the first two pianos:
Cost of manufacturing the 3rd piano = C(3) - C(2)
= $5700 - (Fixed Cost + Marginal Cost * 2)
= $5700 - ($1200 + $1500 * 2)
= $5700 - ($1200 + $3000)
= $5700 - $4200
= $1500
Therefore, the cost of manufacturing the 3rd piano is $1500.
c) The cost of manufacturing the 11th piano that day can be found by directly evaluating C(11):
C(11) = Fixed Cost + (Marginal Cost * Number of Pianos)
= $1200 + ($1500 * 11)
= $1200 + $16500
= $17700
Therefore, the cost of manufacturing the 11th piano is $17700.
To find the cost function, we need to add the fixed cost and the marginal cost.
a) The cost of manufacturing 3 pianos (x=3) can be found by plugging x=3 into the cost function:
C(x) = Fixed cost + (Marginal cost * Number of pianos)
C(3) = $1200 + ($1500 * 3)
= $1200 + $4500
= $5700
Therefore, the cost of manufacturing 3 pianos in one day is $5700.
b) To find the cost of manufacturing the 3rd piano, we need to calculate the cost when x=3 from the cost function:
C(3) = $1200 + ($1500 * 3)
= $1200 + $4500
= $5700
Therefore, the cost of manufacturing the 3rd piano that day is $5700.
c) To find the cost of manufacturing the 11th piano, we again plug x=11 into the cost function:
C(11) = $1200 + ($1500 * 11)
= $1200 + $16500
= $17700
Therefore, the cost of manufacturing the 11th piano that day is $17700.