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romanna [79]
3 years ago
14

A firm has a fixed cost of $500 in its first year of operation. When the firm produces 100 units of output, its total costs are

$3,500. When it produces 101 units of output, its total costs are $3,750. What is the marginal cost of producing the 101st unit of output? a. $250 b. $275 c. $340.91 d. $350
Mathematics
1 answer:
HACTEHA [7]3 years ago
7 0

Answer:

option (a) $250

Step-by-step explanation:

Data provided in the question:

Fixed cost = $500

For 100 units produced Total cost = $3,500

For 101 units produced, Total cost = $3,750

Now,

Marginal cost is calculated as:

Marginal cost = \frac{\textup{Total change in cost of producing more goods}}{\textup{Total change in produced goods}}

thus,

Marginal cost = \frac{\textup{Total cost of 101 units - Total cost of 100 units}}{\textup{101-100}}

or

Marginal cost = \frac{\textup{3,750-3,500}}{\textup{1}}

or

Marginal cost = $250

Hence,

The correct answer is option (a) $250

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Answer:

76 mL of 8% and 304 mL of 13%

Step-by-step explanation:

Set up a table like this (this is the same table for any mixture problem):

                   mL total     *           % vinegar       =              % vinegar/mL

8%

13%

total %

What you do with this table is multiply the first 2 columns and they equal the last column.  We already know the middle column's entries from what we are given.  But remember that a percent needs to be expressed as a decimal:

                       mL total     *       % vinegar      =        % vinegar/mL

8%                                                 .08

13%                                                .13

total %                                  

Now we also know that the total he wants to make is 380 mL that is 12%, so all that info goes into the last row:

                      mL total       *       % vinegar        =        % vinegar/mL

8%                                                   .08

13%                                                  .13

total %            380                          .12

If he wants this total mixture to come from the 8% and the 13% vinegars, he is mixing them together, or adding them.  We need to know how much 8% + how much 13% will give us 380 mL of 12%.  So we can fill in the amounts accordingly.  If he has x mL of 8%, then he will have 380 - x of 13%.  The table tells us that we are multiplying the first 2 columns to get the third, so we will do that at the same time:

                       mL total         *          % vinegar        =        % vinegar/mL

8%                        x                *             .08                =          .08x

13%                 380 - x            *             .13                 =      .13(380 - x)

total %               380              *             .12                 =          45.6

Since we are adding the different vinegars together to get the total, we can do that with the last column as well.  This is our equation:

.08x + .13(380 - x) = 45.6  Multiply everything through by 100 to get rid of the decimals now:

8x + 13(380 - x) = 4560 and

8x + 4940 - 13x = 4560 and

-5x = -380 so

x = 76

This means that there is 76 mL of 8% and 380 - 76 = 304 mL of 13%

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