Question

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).

Answer 1

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