Ask question

Ask question

All categories

21 day ago

15

Sally is hosting an Internet auction to sell n widgets. She receives m bids, each of the form "I want ki widgets for di dollars,

" for i = 1, 2, . . . , m. Characterize her optimization problem as a knapsack problem. Under what conditions is this a 0-1 versus fractional problem?

1 answer:

PIT_PIT [9.1K]21 day ago

5 0

Answer:

Refer to the attachment

Step-by-step explanation:

Refer to the attachment

You might be interested in

Find the point on the circle x^2+y^2 = 16900 which is closest to the interior point (30,40)

Leona [9271]

Response-

(78,104) represents the point closest to the interior.

Explanation-

The equation defining the circle,

$\Rightarrow x^2+y^2 = 16900$

$\Rightarrow y^2 = 16900-x^2$

$\Rightarrow y = \sqrt{16900-x^2}$

Since the point lies on the circle, its coordinates must be,

$(x,\sqrt{16900-x^2})$

The distance "d" from the point to (30,40) can be calculated as,

$=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

$=\sqrt{(x-30)^2+(\sqrt{16900-x^2}-40)^2}$

$=\sqrt{x^2+900-60x+16900-x^2+1600-80\sqrt{16900-x^2}}$

$=\sqrt{9400-60x-80\sqrt{16900-x^2}}$

Next, we need to determine the value of x for which d is minimized. The minimum distance occurs when $9400-60x-80\sqrt{16900-x^2}$ is at its lowest value.

Let’s set up the equation,

$\Rightarrow f(x)=9400-60x-80\sqrt{16900-x^2}$

$\Rightarrow f'(x)=-60+80\dfrac{x}{\sqrt{16900-x^2}}$

$\Rightarrow f''(x)=\dfrac{1352000}{\left(16900-x^2\right)\sqrt{16900-x^2}}$

We find the critical points,

$\Rightarrow f'(x)=0$

$\Rightarrow-60+80\dfrac{x}{\sqrt{16900-x^2}}=0$

$\Rightarrow 80\dfrac{x}{\sqrt{16900-x^2}}=60$

$\Rightarrow 80x=60\sqrt{16900-x^2}$

$\Rightarrow 80^2x^2=60^2(16900-x^2)$

$\Rightarrow 6400x^2=3600(16900-x^2)$

$\Rightarrow \dfrac{16}{9}x^2=16900-x^2$

$\Rightarrow \dfrac{25}{9}x^2=16900$

$\Rightarrow x=\sqrt{\dfrac{16900\times 9}{25}}=78$

$\Rightarrow x=78$

Then,

$\Rightarrow f''(78)=\dfrac{1352000}{\left(16900-78^2\right)\sqrt{16900-78^2}}=\dfrac{125}{104}=1.2$

Since f''(x) is positive, the function f(x) achieves its minimum at x=78

When x is set to 78, the corresponding y value will be

$\Rightarrow y = \sqrt{16900-x^2}=\sqrt{16900-78^2}=104$

This leads us to conclude that the closest point is (78,104)

5 0

1 month ago

Write the standard form of the line that contains a slope of -3/8 and passes through the point (5, -4). Include your work in you

zzz [9080]

The answer with the work has been provided previously.

6 0

1 day ago

Read 2 more answers

If x3=64 and y3=125, what is the value of y−x?

Zina [9171]

Answer: We start with equation 1

x=64/3

Next, we solve equation 2

y=125/3

Now, we combine equations 1 and 2

y-x=125/3 -64/3

=61/3

Step-by-step explanation:

3 0

28 days ago

The perimeter of the triangle is 44cm.if it’s sides are in the ratio 9:7:6.find its area

AnnZ [9099]

Answer:

The area calculates to 83.905 cm^3

Step-by-step explanation:

The overall ratio is 9 + 7 + 6 = 22

Thus, the side lengths are computed as follows;

9/22 * 44 = 18 cm

7/22 * 44 = 14 cm

6/22 * 44 = 12 cm

Heron’s formula allows us to determine the area of the triangle

First, we calculate s

s = (a + b + c)/2 = (18+14+12)/2 = 44/2 = 22

Heron’s formula can be expressed as;

A = √s(s-a)(s-b)(s-c)

where a, b, and c are 18, 14, and 12 respectively

Plugging in the values, we obtain;

A = √22(22-18)(22-14)(22-12)

A = √(22 * 4 * 8 * 10)

A = √(7,040)

A = 83.905 cm^3

3 0

29 days ago

What is the monthly finance charge if the average daily balance is $15, the daily periodic rate is 0.06%, and the number of days

Leona [9271]

Given

The daily average balance is $15.

The daily periodic interest rate = 0.06%.

The cycle consists of 30 days.

Calculate the monthly finance charge.

To justify:

Let’s denote the monthly finance fee as x.

According to the details provided:

The average daily balance = $15.

The daily periodic rate = 0.06%,

First, we convert 0.06% to decimal:

$=\frac{0.06}{100}$

= 0.0006.

Daily finance charge = 0.0006 multiplied by 15.

= 0.009.

The number of days in the cycle totals 30.

Now, calculating the monthly finance charge:

The equation becomes:

x = 15 × 0.0006 × 30.

x = 0.009× 30.

x = $0.27.

Thus, the monthly finance charge amounts to $0.27.

Thus proved.

4 0

17 days ago