Suppose thatthe monthly cost, in dollars, of producing x chairs is C (x) = 0.001x3 + 0.07x2 + 19x + 700, and currently 25chairs are produced monthly.

a.) What isthe current monthly cost?

b.) Whatwould be the additional cost of the increasing production to 26chairs monthly?

c.) What isthe marginal cost when x=25?

d.) usemarginal cost to estimate the difference in cost between producing25 and 27 chairs per month?

e.) Use theanswer from part (d) to predict C (27).

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