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tangare [24]
1 year ago
10

Use calculus to find the first order conditions. Use solver then to solve the first order conditions. Show your work for the fir

st order conditions and include the relevant portion of excel. f(x,y)=-22x^2+22xy-11y^2+110x-40y-23
Mathematics
1 answer:
DaniilM [7]1 year ago
4 0

The values of x and y are 70/22 and 30/22 respectively by using the first-order condition of differential calculus.

<h3>What is the first-order condition in differential calculus?</h3>

A first-order differential equation is represented by the equation \mathbf{ \dfrac{dy}{dx} =f (x,y) }with 2 variables x & y, including its function f(x,y) specified on a xy-plane.

Given that:

\mathbf{f(x,y) =-22x^2+22xy-11y^2+110x-40y-23}

Let us first differentiate the above equation with respect to x, we have:

\mathbf{\dfrac{\partial f(x,y) }{\partial x}  = -44x +22y -0+110-0-0=0}

\mathbf{\implies  -44x +22y+110=0}        (multiply by -1)

44x - 22y = 110    ------ (equation 1)

Now, differentiating with respect to y, we have:

\mathbf{\dfrac{\partial f(x,y) }{\partial y}  =0 +22x-22y +0-40-0=0}

\mathbf{\implies 22x-22y -40=0}

22x - 22y = 40      ----- (equation 2)

Now, we have a system of equations:

44x - 22y = 110

-                      ---- ( subtracting equation 2 from 1; elimination method)

<u> 22x - 22y = 40  </u>

<u>22x    + 0  = 70    </u>

<u />

x = 70/22

Replacing the value of x into equation (1), we have:

44x - 22y = 110

44(70/22) - 22y = 110

140 - 22y = 110

140 - 110 = 22y

30 = 22y

y = 30/22

Learn more about the first-order conditions in differential calculus here;

brainly.com/question/14528981

#SPJ1

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Mariana [72]

Complete Question

In your biology class, your final  grade is based on several things: a lab score, scores on two major tests, and your score on the final exam. There are 100 points available for each score. However, the lab score is worth 25% of your total grade, each major test is worth 22:5%, and the final exam is worth 30%. Compute the weighted average for the following scores: 92 on the lab, 81 on the first major test, 93 on the second major test, and 85 on the final exam. (Enter your answer to one decimal place)

Answer:

The weighted average is  W = 87.65

Step-by-step explanation:

From the question we are told that

  The worth of the lab score is  25% of total grade

  The worth of each major  test is   22.5% of total grade

   The worth of final exam is  30% of total grade

The  score on lab is  92

The score on first major test 81

The score on second major test 93

 The score on final  exam is  85

Generally the weighted score is mathematically represented as

     W = 0.25 *  92 + 0.225* 81 + 0.225* 93 +0.30 * 85

=> W = 0.25 *  92 + 0.225* 81 + 0.225* 93 +0.30 * 85

=> W = 87.65

   

   

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