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Alex Ar [27]
3 years ago
10

Let Upper C left-parenthesis q right-parenthesis represent the cost, Upper R left-parenthesis q right-parenthesis the revenue, a

nd pi left-parenthesis q right-parenthesis the total profit, in dollars, of producing q items.(a) If Upper C prime left-parenthesis 50 right-parenthesis equals 75 and Upper R prime left-parenthesis 50 right-parenthesis equals 88, approximately how much profit is earned by the 51 Superscript st item?The profit earned from the 51 Superscript st item will be approximately_______ dollar-sign.(b) If Upper C prime left-parenthesis 90 right-parenthesis equals 71 and Upper R prime left-parenthesis 90 right-parenthesis equals 67, approximately how much profit is earned by the 91 Superscript st item?The profit earned from the 91 Superscript st item will be approximately______ dollar-sign
Mathematics
1 answer:
Dennis_Churaev [7]3 years ago
4 0

Answer:

(a)$13

(b) Loss of $4

Step-by-step explanation:

C(q) represents Cost of producing q units.

R(q) represents Revenue generated from q units.

P(q) represents Total Profit made from producing q units.

Marginal analysis is concerned with estimating the effect on quantities such as cost, revenue, and profit when the level of production is changed by a unit amount. For example, if C(q) is the cost of producing q units of a certain commodity, then the marginal cost, MC(q), is the additional cost of producing one more unit and is given by the difference

MC(q) = C(q + 1) − C(q).

Using the estimation

C'(q)≈\frac{C(q+1)-C(q)}{(q+1)-q}=C(q+1)-C(q)

We find out that MC(q)=C'(q)

We can therefore compute the marginal cost by the derivative C'(q).

This also holds for Revenue, R(q) and Profit, P(q).

(a) If C'(50)=75 and R'(50)=88

51st item.

P'(50)=R'(50)-C'(50)

=88-75=$13

The profit earned from the 51st item will be approximately $13.

(b) If C'(90)=71 and R'(90)=67, approximately how much profit is earned by the 91st item.

P'(90)=R'(90)-C'(90)

=67-71= -$4

The profit earned from the 91 st item will be approximately -$4.

There was a loss of $4.

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3 years ago
Y = 7/8u + 9, solve for u
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Answer:

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Step-by-step explanation:

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A fluid moves through a tube of length 1 meter and radius r=0.006±0.00025 meters under a pressure p=4⋅105±2000 pascals, at a rat
iris [78.8K]

Answer:

Maximum error for viscosity is 17.14%

Step-by-step explanation:

We know that everything is changing with respect to the time, "r" is changing with respect to the time, and also "p" just "v" will not change with the time according to the information given, so we can find the implicit derivative with respect to the time, and since

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The implicit derivative with respect to the time would be

\frac{dn}{dt}  = \frac{\pi}{8} ( \frac{r^4}{v} \frac{dp}{dt}  + \frac{4pr^3}{v}\frac{dr}{dt} )

If we multiply everything by    dt   we get  

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Remember that  the error is given by   \frac{dn}{n}   therefore doing some algebra we get that

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Since,    r = 0.006   ,   dr = 0.00025 ,  p = 4*105   ,   dp = 2000  we get that

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This should help!! Thanks! Let me know!

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