1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
My name is Ann [436]
3 years ago
8

A printer has a contract to print 100,000 posters for a political candidate. He can run the posters by using any number of plate

s from 1 to 30 on his press. If he uses x metal plates, they will produce x copies of the poster with each impression of the press. The metal plates cost $20.00 to prepare, and it costs $125.00 per hour to run the press. If the press can make 1000 impressions per hour, how many metal plates should the printer make to minimize costs
Mathematics
1 answer:
yulyashka [42]3 years ago
4 0

Answer:

25

Step-by-step explanation:

From the given information;

Numbers of posters that can be printed in an hour = no of impression/hour × no of plate utilized in each impression.

= 1000x

Thus, the required number of hours it will take can be computed as:

\implies \dfrac{100000}{1000x} \\ \\ =\dfrac{100}{x}

cost per hour = 125

If each plate costs $20 to make, then the total number of plate will equal to 40x

∴

The total cost can be computed as:

C(x) = (\dfrac{100}{x}) \times 125 + 20 x --- (1)

C'(x) = (-\dfrac{12500}{x^2})  + 20  --- (2)

At C'(x) = 0

\dfrac{12500}{x^2} = 20

\dfrac{12500}{20} = x^2

x^2= 625

x = \sqrt{625}

x = 25

C'' (x) = -12500 \times \dfrac{-2}{x^3} +0

C'' (x) = \dfrac{25000}{x^3}

where; x = 25

C'' (x) = \dfrac{25000}{25^3}

C''(x) = 1.6

Thus, at x = 25, C'' > 0

As such, to minimize the cost, the printer needs to make 25 metal plates.

You might be interested in
Write this number in word form 310763136
Tresset [83]
Three hundred and ten million seven hundred and sixty three one hundred and thirty six
3 0
3 years ago
Read 2 more answers
Total money of 2 quarters, 1 dime, 3 pennies
Makovka662 [10]
You would have sixty three cents
8 0
2 years ago
Read 2 more answers
Let f(x) = -8x + 4 and g(x) = 3x2 + 5. Find f(7) + g(7) .
VMariaS [17]

Answer:

-7

Step-by-step explanation:

substitute both x's for 7:

(-8(7)+4)+ (3(7)2+5)

= -54 + 47

= -7

6 0
2 years ago
16 to the second power - 14 to the second power - g =6
jarptica [38.1K]
16X16=256-196=60-6=54
7 0
3 years ago
On an airplane,there are two seats on the left in each row and three on the right side.There are 90 seats on the right side of t
Oksana_A [137]

Answer:

A) 60

B) 150

Step-by-step explanation:

5 0
3 years ago
Other questions:
  • What is the value of x? Enter your answer in the box.
    12·2 answers
  • The simple interest formula is I = Prt, where I represents simple interest on an amount, P, for t years at a rate of r, where r
    8·1 answer
  • Determine the slope of the line that has the following coordinates: (1.5, 6) (3.75, -12)
    5·2 answers
  • Plz helppppp!!!! Thanks
    14·1 answer
  • Find the simple interest earned on a deposit of $2,800 that earns 2% annual interest after 5 years.
    7·1 answer
  • Can someone please help its due soon.
    5·2 answers
  • I need help<br> please someone
    13·1 answer
  • Choose Yes or No to tell if each statement is true.
    9·2 answers
  • In the song, 7 pounds, 5 ounces was the median weight of the students at birth. Which of these is correct?
    7·2 answers
  • Mario and his 3 friends attend a professional football game after parking tickets and food they spent 240 total Mario tells his
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!