Answer:
Given the cost function of chair produced monthly as
C(x) =0.001x³ + 0.07x² + 19x +700
where x =no of chairs produced
a) Current monthly cost?
For x=25, C = 0.001 (25)³ + 0.07(25)² + 19(25) +700
C = 15.625+43.75+475+700
C = $1234.38
b) additional cost of the increasing production to 26 chairs monthly?
that is C(26) - C(25) = ?
For C(26) = 0.001 (26)³ + 0.07(26)² + 19(26) +700
C(26) =$1258.89
C(26) - C(25) = $24.52
c) the marginal cost when x=25?
This is dC/dx = 0.003x² + 0.14x +19
Marginal Cost at x =25, = 0.003(25)² + 0.14(25) +19
= $24.375/chair
d) To estimate the difference in cost between producing 25 and 27 chairs per month?
we will find dC/dx(27)?
Marginal Cost at x =27, = 0.003(27)² + 0.14(27) +19
C(27) = $81.83/chair
For increase in chairs per month = 2,
The difference in cost between C(25) and C(27), = ($81.83 - $24.375) x 2 =$114.91
e) To predict C(27) = ?
From (d) to predict this, it means for a single chair, we have the cost as $57.454/chair
so for 27 chairs, the cost will be $57.454 x 27 = $1551.26/month
