Thank you! The table shows the marginal cost for a company\'s product at various

Question

Thank you!

The table shows the marginal cost for a company's product at various production levels. Marginal cost Marginal cost Units ($/unit) Units ($/unit) 3.21 7000 2.15 100 2.89 8000 2.14 200 2.77 9000 2.16 300 2.71 10,000 2.20 400 2.59 11,000 2.34 500 2.47 12,000 2.64 13,000 2.84 600 2.21 (a) Estimate the cost (not including fixed costs) to produce the first 12,000 units by considering batches of 2000 units. Use the initial marginal cost for each batch in your calculations. (b) Use batches of 1000 units and the ending marginal cost for each batch to estimate the cost of raising the production level from 4000 to 11,000 units.

Explanation / Answer

( 5 )

given

( 0 , 10 ) f(x) dx

for x < 8 f(x) = 8

for x >=8 f(x) = x

( 0 , 8 ) f(x) dx +   ( 8 , 10 ) f(x) dx

==>   ( 0 , 8 ) 8 dx +   ( 8 , 10 ) x dx

==> 8 x ( 0 , 8 ) + x^2/2 ( 8 , 10 )

==>8 ( 8 - 0 ) + ( 10^2 - 8 ^2 ) /2

==> 64 + ( 100 - 64 ) /2

==> 64 + ( 36) /2

==> 64 + 18 ==> 82

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