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2 years ago

Which ordered pair minimizes the objective function C = 60x + 85y?

Mathematics

1 answer:

Paha777 [63]2 years ago

5 0

Answer:

the that minimizes the function is (80, 50) for which C = 9050

Step-by-step explanation:

(0, 160). (55, 70). (80, 50). (170, 0)..... available pairs missing out in the question

Step 1: to get the pair that minimizes the objective function C = 60x + 85y, we plug in each pair and work out the minimum value of C.

(0, 160): C = (60*0) + (85*160) = 13600

(55, 70): C = (60*55 + (85*70) = 9250

(80, 50): C = (60*80) + (85*50) = 9050

(170, 0): C = (60*170) + (85*0) = 10200

Hence the minimum value of C occur at (80, 50)

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EXAMPLE 5 If F(x, y, z) = 4y2i + (8xy + 4e4z)j + 16ye4zk, find a function f such that ∇f = F. SOLUTION If there is such a functi

Valentin [98]

If there is such a scalar function f, then

$\dfrac{\partial f}{\partial x}=4y^2$

$\dfrac{\partial f}{\partial y}=8xy+4e^{4z}$

$\dfrac{\partial f}{\partial z}=16ye^{4z}$

Integrate both sides of the first equation with respect to x :

$f(x,y,z)=4xy^2+g(y,z)$

Differentiate both sides with respect to y :

$\dfrac{\partial f}{\partial y}=8xy+4e^{4z}=8xy+\dfrac{\partial g}{\partial y}$

$\implies\dfrac{\partial g}{\partial y}=4e^{4z}$

Integrate both sides with respect to y :

$g(y,z)=4ye^{4z}+h(z)$

Plug this into the equation above with f , then differentiate both sides with respect to z :

$f(x,y,z)=4xy^2+4ye^{4z}+h(z)$

$\dfrac{\partial f}{\partial z}=16ye^{4z}=16ye^{4z}+\dfrac{\mathrm dh}{\mathrm dz}$

$\implies\dfrac{\mathrm dh}{\mathrm dz}=0$

Integrate both sides with respect to z :

$h(z)=C$

So we end up with

$\boxed{f(x,y,z)=4xy^2+4ye^{4z}+C}$

7 0

2 years ago

A small company's net income for the first six months of the year was $76,500 and for the last six months it was $100,000 what i

Talja [164]

The correct answer is:

153/200.

Explanation:

The amount for the first 6 months is 76500 and the amount for the last 6 months is 100000. This makes the ratio 76500/100000.

Both of these end with two 0's; this means they are both divisible by 100. 76500/100 = 765 and 100000/100 = 1000; this makes the ratio 765/1000.

Since these end with a 5 or a 0, they are divisible by 5; 765/5 = 153 and 1000/5 = 200; this makes the ratio 153/200.

153 is only divisible by 3 or 9; 153/3 = 51 and 153/9 = 17. None of these will divide evenly into 200, so we stop at 153/200.

4 0

2 years ago

Read 2 more answers

In ΔFGH, f = 37 cm, ∠F=28° and ∠G=124°. Find the length of g, to the nearest 10th of a centimeter.

MatroZZZ [7]

Answer:

65.3 cm

Step-by-step explanation:

The law of sines can be used for this.

g/sin(G) = f/sin(F)

g = (37 cm)sin(124°)/sin(28°) ≈ 65.3 cm . . . . multiply by sin(G)

The length of g is about 65.3 cm.