Question

Suppose that the monthly cost, in dollars, of producing x chairs is C(x) = 0.006x^3 + 0.07x^2 + 19x + 700, and currently 35 chairs are produced monthly. a) What is the current monthly cost? b) What would be the additional cost of increasing production to 38 chairs monthly? c) What is the marginal cost when x = 35? d) Use the marginal cost to estimate the difference in cost between producing 35 and 37 chairs per month. d) Use the answer from part (d) to predict C(37). a) The current monthly cost is $ b) The additional cost of increasing production to 38 chairs monthly is $ c) The marginal cost when x = 35 is $ d) Using the marginal cost found in part c), the difference between producing 35 and 37 chairs per month is $ e) C(37) = $

Answer 1

Answer:

a) The current monthly cost is :  1193.50 $

b) The additional cost of producing 38 units instead of 35 is 0.35 $

c) Marginal cost of producing  the 35 unit is   1.85 $

d) difference between producing 35 and 37 units per month is

1193.85- 1.85 =  2 $

e) C(37) = 1194.91 $

Step-by-step explanation:

a) Monthly cost is:

C(x)  = - 0.006 *x³  + 0.07* x² + 19*x + 700

If company produces 35 units per month, the current monthly cost would be: 0.35 $

C(35)  =  - 0.006*x³ + 0.07* x² + 19*x + 700

C(35)  =  - 0.006* (35)³ + 0.07* (35)² + 19* (x) + 700

C(35)  =  - 257.25 + 85.75 + 665 +  700

C(35)  =  1193.50 $

b) We have to find the current cost of 38 units

C(38) =  -0.006*(38)³ + 0.07 *(38)² + 19*38 + 700

C(38) =  - 329.23 + 101.08  +   722 + 700

C(38) =  1193.85

Then   C(38)  - C (35)      ⇒  1193.85 - 1193.50  =  0.35 $

c) Marginal cost when x = 35

Current monthly cost

C(x) = - 0.006 *x³  + 0.07* x² + 19*x + 700

Then Marginal cost is

C´(x) = - 3* 0.006* x² +  2*0.07*x  + 19  

for  x  =  35 marginal cost would be:

C´(35)  =  - 0.018*(35)²  +  0,14 *(35) * 19

C´(35)  =  - 22.05  +  4.9 + 19

C´(35)  =  1.85 $

d) The current cost of producing 38 units is  1193.85 $ then difference between producing 35 and 37 units per month is

1193.85- 1.85 =  2 $

e) The cost of producing 37 units per month is:

C(37) =  - 0.006*(37)³ +  0.07*(37) + 19*(37) + 700

C(37) =  -- 303.92  +  95.83 +  703 + 700

C(37) = 1194.91