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3 years ago

5

A company finds that if they price their product at $ 35, they can sell 225 items of it. For every dollar increase in the price,

the number of items sold will decrease by 5.
What is the maximum revenue possible in this situation? (Do not use commas when entering the answer) $

What price will guarantee the maximum revenue? $

1 answer:

Basile [38]3 years ago

8 0

Answer:

Maximum revenue = $8000

The price that will guarantee the maximum revenue is $40

Step-by-step explanation:

Given that:

Price of product = $35

Total sale of items = 225

For every dollar increase in the price, the number of items sold will decrease by 5.

The total cost of item sold = 225 ×35

The total cost of item sold = 7875

If c should be the dollar unit in price increment;

Therefore; the cost function is : $[35+c(1)][225-5(c)]$

For maximum revenue;

$\dfrac{d}{dc}(cost \ function) =0$

$\dfrac{d}{dc}[[35+c(1)][225-5(c)]]=0$

0+225-35× 5 -10c = 0

225 - 175 =10c

50 = 10c

c = 50/10

c = 5

Maximum revenue = $[35+c(1)][225-5(c)]$

Maximum revenue = $[35+5(1)][225-5(5)]$

Maximum revenue = (35 + 5)(225-25)

Maximum revenue = (40 )(200)

Maximum revenue = $8000

The price that will guarantee the maximum revenue is :

=(35 +c)

= 35 + 5

= $40

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Solution :

We know that

$H_0: \mu_1 = \mu_2=\mu_3$

$H_1 :$ At least one mean is different form the others (claim)

We need to find the critical values.

We know k = 3 , N = 35, α = 0.05

d.f.N = k - 1

= 3 - 1 = 2

d.f.D = N - k

= 35 - 3 = 32

SO the critical value is 3.295

The mean and the variance of each sample :

Goust Jet red Cloudtran

$\overline X_1 =50.5$ $\overline X_2 =50.07143$ $\overline X_3 =55.71429$

$s_1^2=19.96154$ $s_2^2=14.68681$ $s_3^2=36.57143$

The grand mean or the overall mean is(GM) :

$\overline X_{GM}=\frac{\sum \overline X}{N}$

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= 52.1714

The variance between the groups

$s_B^2=\frac{\sum n_i\left( \overline X_i - \overline X_{GM}\right)^2}{k-1}$

$=\frac{\left[14(50.5-52.1714)^2+14(52.07143-52.1714)^2+7(55.71426-52.1714)^2\right]}{3-1}$

$=\frac{127.1143}{2}$

= 63.55714

The Variance within the groups

$s_W^2=\frac{\sum(n_i-1)s_i^2}{\sum(n_i-1)}$

$=\frac{(14-1)19.96154+(14-1)14.68681+(7-1)36.57143}{(14-1)+(14-1)+(7-1)}$

$=\frac{669.8571}{32}$

= 20.93304

The F-test statistics value is :

$F=\frac{s_B^2}{s_W^2}$

$=\frac{63.55714}{20.93304}$

= 3.036212

Now since the 3.036 < 3.295, we do not reject the null hypothesis.

So there is no sufficient evidence to support the claim that there is a difference among the means.

The ANOVA table is :

Source Sum of squares d.f Mean square F

Between 127.1143 2 63.55714 3.036212

Within 669.8571 32 20.93304

Total 796.9714 34

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3 years ago

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siniylev [52]

Answer:

B E F G

Step-by-step explanation:

Polygons are 2 dimensional shapes with straight edges (no curved edges). The shape needs to be closed up entirely to be a polygon. It cannot have any intersecting line segments

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I can't be a polygon because polygons cannot have intersecting lines

J can't be a polygon because polygons cannot have intersecting lines

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