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
Ad libitum [116K]
3 years ago
10

Nemecek Brothers make a single product on two separate production lines, A and B. Its labor force is equivalent to 1000 hours pe

r week, and it has $3000 outlay weekly on operating costs. It takes 1 hour and 4 hours to produce a single item on lines A and B, respectively. The cost of producing a single item is $5 on line A and $4 on line B. (a) Write the inequality that expresses the labor information. (b) Write the inequality that expresses the cost information.
Mathematics
1 answer:
frez [133]3 years ago
8 0

Answer:

(a) The inequality for the number of items, x, produced by the labor, is given as follows;

250 ≤ x ≤ 600

(b) The inequality for the cost, C is $1,000 ≤ C ≤ $3,000

Step-by-step explanation:

The total time available for production = 1000 hours per week

The time it takes to produce an item on line A = 1 hour

The time it takes to produce an item on line B = 4 hour

Therefore, with both lines working simultaneously, the time it takes to produce 5 items = 4 hours

The number of items produced per the weekly labor = 1000/4 × 5 = 1,250 items

The minimum number of items that can be produced is when only line B is working which produces 1 item per 4 hours, with the weekly number of items = 1000/4 × 1 = 250 items

Therefore, the number of items, x, produced per week with the available labor is given as follows;

250 ≤ x ≤ 1250

Which is revised to 250 ≤ x ≤ 600 as shown in the following answer

(b) The cost of producing a single item on line A = $5

The cost of producing a single item on line B = $4

The total available amount for operating cost = $3,000

Therefore, given that we can have either one item each from lines A and B with a total possible item

When the minimum number of possible items is produced by line B, we have;

Cost = 250 × 4 = $1,000

When the maximum number of items possible, 1,250, is produced, whereby we have 250 items produced from line B and 1,000 items produced from line A, the total cost becomes;

Total cost = 250 × 4 + 1000 × 5 = 6,000

Whereby available weekly outlay = $3000, the maximum that can be produced from line A alone is therefore;

$3,000/$5 = 600 items = The maximum number of items that can be produced

The inequality for the cost, C, becomes;

$1,000 ≤ C ≤ $3,000

The time to produce the maximum 600 items on line A alone is given as follows;

1 hour/item × 600 items = 600 hours

The inequality for the number of items, x, produced by the labor, is therefore, given as follows;

250 ≤ x ≤ 600

You might be interested in
Use the Distributive Property to rewrite the expression 5ax + 5ay as an equivalent expression.
KengaRu [80]

Answer:

5ax + 5ay = 5a(x+y)

Step-by-step explanation:

6 0
3 years ago
Dr Adams is a botanist.she measures the daily height of a particular of sunflower is 60 days old.at 60 days,the height of the su
dexar [7]
Lets write a linear equation to represent this flower growth, lets call y the height of the flower in centimeters and x the number of days passed:
y = 205 + 2x
that means that the flower height y, will grow 2 centimeterrs each x days.
So if we have 235 cm height, we can find the amount of days needed if we replace in the equation and solve for x:
<span>y = 205 + 2x
</span>235 = 205 + 2x
2x = 235 - 205
2x = 30
x = 15
therefore the flower needs 15 days to reach 235 cm height
5 0
3 years ago
A rectangle board is 1.2 meters long and 0.8 meters wide. What is the area of the board in millimeters
ivanzaharov [21]

Answer:

1200*800 = 960,000 mm²

Step-by-step explanation:

1 meter is 1000 mm and 0.8 meter is 800 mm

A=lw

5 0
3 years ago
Find the indicated angle please help (multiple choice)
Taya2010 [7]

Answer:

D

Step-by-step explanation:

sohcahtoa

Sin x = 32/58

sin x = .5517

x = 33°

3 0
3 years ago
During hibernation a garter snake's body temperature never goes below 3 C write and graph an inequality that represents this sit
Akimi4 [234]
>3c
because it never goes BELOW which is why you put the sign

3 0
3 years ago
Other questions:
  • What number should be added to both sides of the equation to complete the square?
    13·2 answers
  • At a store, apples cost $5 for 2 pounds. Which of these is the value of the ratio of dollars to pounds of apples?
    12·2 answers
  • please help me , this is the third one i have posted like this , if someone can go and help me on all of these is appreciate it
    8·1 answer
  • Traffic police measure the speed of the incoming vehicles. The speeds are normally distributed with a mean of 70 km/hr and a sta
    5·1 answer
  • Robert (R) is 4 less than twice Liz’s (L) age. Write the equation that represents Robert’s age.
    7·1 answer
  • Besides math name a reason why someone would need to find the volume of a cone, and a prism?
    14·1 answer
  • 9^5•9^8 rewrite the following expression using each base only once
    6·1 answer
  • Find the perimeter of the triangle. <br> A) 20 <br> B) 51 <br> C) 12 + 74 <br> D) 12 + 47
    6·2 answers
  • A salesperson at a jewelry store earns 3​% commission each week. Last​ week, Heidi sold $450 worth of jewelry. How much did she
    5·2 answers
  • Pythagorean Theorem with Known Legs
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!