A manufacturer of kitchen appliances is preparing to set the price on a new blender. Demand is thought to depend on the price and is represented by the model D=2,000 - 4P. The accounting department estimates that the total costs can be represented by C = 6,000+ 3D. Develop a model for the total profit. Implement the model on a spreadsheet and use nonlinear optimization with Solver to find the price that maximizes profit.
The price that maximizes profit is P = $
(Round to the nearest cent as needed.)

Answer:

The price that maximize profit is P = $251.5

Step-by-step explanation:

The given function for the demand, D = 2,000 - 4·P

The function that represent the total cost, C = 6,000 + 3·D

Therefore, the revenue, R = P × D = P × (2,000 - 4·P) = 2000·P - 4·P²

The cost, C = 6000 + 3·D = 6,000 + 3 × (2,000 - 4·P) = 12,000 - 12·P

The profit, Pr = R - C = 2000·P - 4·P² - (12,000 - 12·P) = 2,012·P - 12,000 - 4·P²

∴ The profit, Pr = 2,012·P - 12,000 - 4·P²

Implementing the model on MS Excel with the Solver app, by implementing the following steps;

1) Enter a value for a price into a cell on MS Excel for example A1

2) Enter the equation into another cell on MS Excel by the first cell, entering the equal to sign, '=', before the equation while replacing 'P' in the original equation with the name of the price cell as follows;

'= 2012*A1 - 12000 - 4*A1^2

3) Ensure that the Solver Add-In is enabled on MS Excel from within the Options dialogue box opened from the Files menu

4) Select the Data tab then select Solver to open the Solver dialog box

5) For the Set Objective select the cell containing the formula then for the By Changing Variable Cells box, select cell A1

6) Ensure that Max is selected in the To options then select Solve; The maximum value will be displayed in the formula cell while the price that gives the maximum value will be displayed in A1

From MS Excel Solver application, the price that gives the maximum profit is P = $251.5

Please answer this! 100 Points!

Divide. Round your answer to the nearest hundredth.

A sample of 100 women is obtained, and their heights (in inches) and pulse rates (in beats per minute) are measured. The linear correlation coefficient is 0.239 and the equation of the regression line is y = 18.5 + 0.890x, where x represents height. The mean of the 100 heights is 62.9 in and the mean of the 100 pulse rates is 73.4 beats per minute. Find the best predicted pulse rate of a woman who is 65 in tall. Use a significance level of α=0.01 The best predicted pulse rate of a woman who is 65 in tall is_______beats per minute.. (Round to two decimal places as needed.) Answer

−30=7r+5 I need to show work too

What was the total distance, in miles, Eil has biked when he finally reached the library?

in what way is five groups of two different from two groups of five ?

estimate, i need help asap

Which value belongs in the box

Four pounds of bananas cost $6. What is the cost per pound of bananas?

Question 7 options:

$24 per pound


$1.50 per pound


$1 per pound


$6 per pound

4 x 10^8 + 8x10^7 ?

please please ASAP please

GET THIS RIGHT AND GET BRAINLESS I NEED HELP!!!! Find the Greatest Common Factor (GCF) of the following numbers: 72 120​

The steady growth line best supports which conclusion about the economy
represented in the graph?
The Business Cycle
Production output
Time
O A. The economy does not show a consistent pattern in its business
cycles.
O B. The economy is weak and will likely enter a depression in the next
business cycle.
O C. The economy has more pronounced peaks than valleys in each
business cycle.
O D. The economy as a whole continues to grow between each
business cycle.

For which inequality would x = 12 be a solution? x + 4s 12 12 = x= 12 12 - X 2 4 12 x < 200​

Shandra has a bag that contains orange chews, cherry chews, and watermelon chews.
She performs an experiment. Shandra randomly removes a chew from the bag,
records the result, and returns the chew to the bag. Shandra performs the experiment
78 times. The results are shown below:
An orange chew was selected 42 times.
A cherry chew was selected 14 times.
A watermelon chew was selected 22 times.
Based on these results, express the probability that the next chew Shandra removes
from the bag will be watermelon chew as a percent to the nearest whole number.

AHHHhHhHhHHhhHHHhHH!!!!!!!!

18.) What do you think would happen to the median if we included students
from grades 10-12?
(Please help it’s a literal kid life crisis )

Geh aahhahahahahaha

Ahahahdhdkrhrvfh

The temperature in Chicago over 5 days were -5,0,4,-1,-3. Which list shows these temperatures arranged from least to greatest

PLEASE HELP (NO LINKSS THEY WILL GET REPORTED)

Dai orders milk with her meal. The server asks her if she wants regular or chocolate. Dai can choose from skim, 2%, or whole, and from small, medium, or large. If all of the choices are equally likely to be ordered, what is the probability that Dai orders a regular, medium milk? Use a tree diagram to solve.

A rectangle measures 12cm by 4cm.
What is its area?

Kristen takes a piece of wood that is 1 inch thick and glues it to a piece of wood that is 2/12
of an inch thick. Together, what is the thickness of the two pieces of wood?
Write your answer as a fraction or as a whole or mixed number.

Please help I’ll mark you as brainliest if correct!

help me guys...the following charts .time;07:30-09:00,09:01-0-30,20:31-12-00,12:01,13:30 mby to AR..850,800,750,600 mby to tbr 1100,2350,1870,1500 mby to ar 620,1400,980,790...... question no 1. what is percentage of passengers traveling between 10:31-12:00 where going to tabora​

Points R(-6,-5), S(-2,-5), and T(-2,n) are plotted in the coordinate plane. The distance between points R and S is half of the distance between points S and T

I’ll give points and brainalist for correct answer (:

Please help me ASAP!!!​

Please help me with my question ASAP please please ASAP ASAP please please help please please ASAP please please help please

I need help asap! Please