MathAdmin at 19:40, 20 April 2015

2015-04-20T19:40:35Z

MathAdmin: Created page with "Find the marginal cost to produce one more item if the fixed cost is $400, the variable cost formula is $x^{2}+30x$ ,..."

2015-04-14T03:44:41Z

Created page with "<span class="exam">Find the marginal cost to produce one more item if the fixed cost is $400, the variable cost formula is <math style="vertical-align: -5%">x^{2}+30x</math>,..."

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<span class="exam">Find the marginal cost to produce one more item if the
fixed cost is $400, the variable cost formula is <math style="vertical-align: -5%">x^{2}+30x</math>,
and the current production quantity is 9 units.

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Foundations:  
|-
|Recall that the total cost, <math>C(x)</math>, is the sum of the fixed and variable costs. Also, the marginal cost at <math style="vertical-align: -20%">x_0</math> units is defined to be the effective cost of the next unit produced, and is precisely <math style="vertical-align: -22%">C'(x_0)</math>.
|}

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
!Solution: 
|-
|Note that
|-
|
::<math>C(x)\,\,=\,\,\mbox{fixed costs + variable costs}\,\,=\,\,400+x^2+30x.</math>
|-
|The expression of the marginal cost is then
|-
|
::<math>C'(x)\,\,=\,\,2x+30.</math>
|-
|Finally, at a production quantity of 9 units, we have the marginal cost
|-
|
::<math>C'(9)\,\,=\,\,2(9)+30\,\,=\,\,58.</math>
|-
|Hence, the marginal cost at a production quantity of 9 units is $58.
|}
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
!Final Answer:  
|-
|The marginal cost at a production quantity of 9 units is $58.
|}
[[022_Exam_1_Sample_A|'''<u>Return to Sample Exam</u>''']]

@@ Line 25: / Line 25: @@
 |-
+|
-::<math>C'(9)\,\,=\,\,2(9)+30\,\,=\,\,58.</math>
+::<math>C'(9)\,\,=\,\,2(9)+30\,\,=\,\,48.</math>
 |-
-|Hence, the marginal cost at a production quantity of 9 units is $58.
+|Hence, the marginal cost at a production quantity of 9 units is $48.
 |}
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 !Final Answer: &nbsp;
 |-
-|The marginal cost at a production quantity of 9 units is $58.
+|The marginal cost at a production quantity of 9 units is $48.
 |}
 [[022_Exam_1_Sample_A|'''<u>Return to Sample Exam</u>''']]

022 Exam 1 Sample A, Problem 9 - Revision history

MathAdmin at 19:40, 20 April 2015

MathAdmin: Created page with "Find the marginal cost to produce one more item if the fixed cost is $400, the variable cost formula is x^{2}+30x,..."

MathAdmin: Created page with "Find the marginal cost to produce one more item if the fixed cost is $400, the variable cost formula is $x^{2}+30x$ ,..."