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
liubo4ka [24]
2 years ago
10

Suppose the firm in this example considers a second product that has a unit profit of $5 and requires 2 hours of production time

for each unit produced. Use y as the number of units of product 2 produced.
Show the mathematical model when both products are considered simultaneously. Express your answers in terms of x and y.
Mathematics
1 answer:
user100 [1]2 years ago
5 0

The question is incomplete, here is the complete question

Recall the production model from Section 1.3:

Max 10x

s.t. 5x ≤ 40

x ≥ 0

Suppose the firm in this example considers a second product that has a unit profit of $5 and requires 2 hours for each unit produced. Assume total production capacity remains 40 units. Use y as the number of units of product 2 produced. . Show the mathematical model when both products are considered simultaneously.

Answer:

Max Profit: 10x + 5y

5x + 2y ≤ 40

x ≥ 0, y ≥ 0

Explanation:

x= number of units of product 1 produced

y = number of units of product 2 produced

Since the first product, x, has a unit profit of $10 and Max1 is 10x

Second product, y, has a unit profit of $5, Max2 = 5y

The maximum profit when both products are considered simultaneously is 10x + 5y

Max Profit = 10x + 5y

Time required for each unit of x is 5hours

Therefore, time required for x units is 5x hours

Time required for each unit of y is 2hours  

Therefore, time required for y units is 2y hours

Time required for the simultaneous production of both products is 5x + 2y

Since production capacity remains 40 units, 5x+2y ≤40

NB: The values of x and y cannot be negative  

You might be interested in
Please help? I’m super lost...
babunello [35]

Answer:

Step-by-step explanation:

In all of these problems, the key is to remember that you can undo a trig function by taking the inverse of that function.  Watch and see.

a.  sin2\theta =-\frac{\sqrt{3} }{2}

Take the inverse sin of both sides.  When you do that, you are left with just 2theta on the left.  That's why you do this.

sin^{-1}(sin2\theta)=sin^{-1}(-\frac{\sqrt{3} }{2} )

This simplifies to

2\theta=sin^{-1}(-\frac{\sqrt{3} }{2} )

We look to the unit circle to see which values of theta give us a sin of -square root of 3 over 2.  Those are:

2\theta =\frac{5\pi }{6} and

2\theta=\frac{7\pi }{6}

Divide both sides by 2 in both of those equations to get that values of theta are:

\theta=\frac{5\pi }{12},\frac{7\pi }{12}

b.  tan(7a)=1

Take the inverse tangent of both sides:

tan^{-1}(tan(7a))=tan^{-1}(1)

Taking the inverse tangent of the tangent on the left leaves us with just 7a.  This simplifies to

7a=tan^{-1}(1)

We look to the unit circle to find which values of <em>a</em> give us a tangent of 1.  They are:

7\alpha =\frac{5\pi }{4},7\alpha =\frac{\pi }{4}

Dibide each of those equations by 7 to find that the values of alpha are:

\alpha =\frac{5\pi}{28},\frac{\pi}{28}

c.  cos(3\beta)=\frac{1}{2}

Take the inverse cosine of each side.  The inverse cosine and cosine undo each other, leaving us with just 3beta on the left, just like in the previous problems.  That simplifies to:

3\beta=cos^{-1}(\frac{1}{2})

We look to the unit circle to find the values of beta that give us the cosine of 1/2 and those are:

3\beta =\frac{\pi}{6},3\beta  =\frac{5\pi}{6}

Divide each of those by 3 to find the values of beta are:

\beta =\frac{\pi }{18} ,\frac{5\pi}{18}

d.  sec3\alpha =-2

Let's rewrite this in terms of a trig ratio that we are a bit more familiar with:

\frac{1}{cos(3\alpha) } =\frac{-2}{1}

We are going to simplify this even further by flipping both fraction upside down to make it easier to solve:

cos(3\alpha)=-\frac{1}{2}

Now we will take the inverse cos of each side (same as above):

3\alpha =cos^{-1}(-\frac{1}{2} )

We look to the unit circle one last time to find the values of alpha that give us a cosine of -1/2:

3\alpha =\frac{7\pi}{6},3\alpha  =\frac{11\pi}{6}

Dividing both of those equations by 3 gives us

\alpha =\frac{7\pi}{18},\frac{11\pi}{18}

And we're done!!!

8 0
2 years ago
Complete the factored form.<br> 7x² +37x + 10 = (7x + 2)()
Ira Lisetskai [31]
The completed factor is (7x+2) (x+5)

7 0
3 years ago
Math question can somebody please help me with this math problem
Elodia [21]
You need to add up all the sides of the thing thank you
5 0
3 years ago
Read 2 more answers
Given two points (2, 7) and (1, -2) on a line, calculate the slope of the line.
Kipish [7]

Answer:

Step-by-step explanation:

Slope of line passing through (2, 7) and (1, -2) = (-2-7)/(1-2) = 9

7 0
2 years ago
How many inches are in 4 1/2 feet ?
mixas84 [53]

Answer:

54.

Step-by-step explanation:

(self-explanatory.)

7 0
2 years ago
Read 2 more answers
Other questions:
  • Starting at sea level, a submarine descended at a constant rate to a depth of −56 mile relative to sea level in 4 minutes. What
    12·2 answers
  • Evaluate the expression by using the given values of the variables.
    15·1 answer
  • the equation a= 180(n-2)/n represents the angle measures, a, in a regular n-sided polygon. When the equation is solved for n, n
    11·2 answers
  • The length of an object object in feet is equal to 3 times it’s linked in yards the length of wall water side slide is 48 feet r
    11·1 answer
  • Can y’all give me strategies(the way you hadit click) y’all have done to remember math.
    7·1 answer
  • Challenger Elementary School has 800 students. Every Wednesday, 12 percent of the students stay after school for Chess Club. How
    5·1 answer
  • What is 2222+(345.234) then divided by 22 Will give brainlyest
    10·1 answer
  • What is the lower fence of this data set?A) 20.5 B) 18 C) 20 D) 19.5
    15·1 answer
  • ANSWER ASAP WILL GIVE BRAINLIEST PLS HELP
    13·1 answer
  • Whats 9+10= help will give brainlist
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!