Question

The marginal cost of producing x units of a certain product is 72 + 1.1x − 0.007x2 + 0.00004x3 (in dollars per unit). Find the increase in cost if the production level is raised from 1800 units to 2000 units. (Round your answer to two decimal places.)

Answer 1

The increase in cost is $81620.

Explanation:

Given:

The marginal cost of producing 'x' units of a certain product is given as:

`C= 72+1.1x-0.007x^2 + 0.00004x^3`

Where, 'C' is the marginal cost.

Now, when
`x=1800\ units`, the marginal cost is given as:

`C_1=72+1.1(1800)-0.007(1800)^2+0.00004(1800)^3\\\\C_1=72+1980-22680+233280\\\\C_1=\$212652`

Again, when
`x=2000\ units`, the marginal cost is given as:

`C_2=72+1.1(2000)-0.007(2000)^2+0.00004(2000)^3\\\\C_2=72+2200-28000+320000\\\\C_2=\$294272`

Now, increase in cost is equal to the difference of the above two costs calculated. Therefore,

`\Delta C= C_2-C_1=\$294272-\$212652=\$81620`

Therefore, the increase in cost is $81620.