the four-step process to find R'(x). the revenue and the instantaneous rate of change of revenue at a production level of 1,000 car seats, and the average change in revenue if production is changed from 1,000 car seats to 1,050 car seats. nd to one decimal place as needed.)
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- A company has determined that its profit for a product can be described by a linear function. The profit from the production and sale of 150 units is $455, and the profit from 250 units is $895. What is the average rate of change of the profit for this product when between 150 and 250 units are sold? Write the equation of the profit function for this product How many units give break-even for this product?The sales function for a product is given by S(x)=119+40.5x2−0.5x3 where x represents thousands of dollars spent on advertising, 0≤x≤54 and S is in thousands of dollars.x Find the point of diminishing returns. Enter the amount spent on advertising as well as the sales in dollars. Amount Spent on Advertising:$ ____ total Sales: $___A company finds that there is a linear relationship between the amount of money that it spends on advertising and the number of units it sells. If it spends no money on advertising it sells 250 units. For each additional $2500 spent, an additional 25 units are sold. 1. If x is the amount of money that the company spends on advertising, find a formula for y, the number of units sold as a function of x. y= 2. How many units does the firm sell if it spends $25,000 on advertising? = ____ units 3. How many units does the firm sell if it spends $50,000 on advertising? = ____ units 4. How much advertising money must be spent to sell 700 units? = _____$ 5. Which of the following statements CORRECTLY explains the meaning of the slope? (select all as there may be more than one correct statment) A. If the company spends an additional $1000 on advertising, it will increases the number of units it sells by 10 . B. If the company increases the amount of money it spends on advertising by $250, it…
- A small company produces organic cookies. When the price is $6 per dozen, the average daily sales has been 72 dozen cookies. When the price was decreased to $3 per dozen, the average daily sales increased to 110 dozen cookies. Assume that daily cookie sales is linearly related to price per dozen. Each dozen cookies has a variable cost of 87 cents to make, plus additional daily fixed costs of $84. Find a function that models the daily profit in terms of the sales x in dozens of cookies.A store owner specializes in connoisseur coffee blends and wants to make 1 kilogram bags that will sell for $ 120 using Colombian, Brazilian and Kenyan coffees. The cost per kilogram of these three types of coffee is $ 140, $ 70, $ 100, respectively. x=Colombian y=Brazilian z=Kenyan Find: The solution of the system of linear equations:DERIVATIVE In the following the symbol for the first derivative is dy/dx or Y’ and the symbol for the second derivative is d2y/dx2 or Y”, all of which are standard symbols. Y = X3 -2X2 +1 X -.333 0 .333 .667 1 1.333 1.667 Y dy/dx d2y/dx2 A function is given above. The table gives several pre-selected values of the independent variable (X). Use all of these to have enough to answer questions for this assignment. Calculate the Y value corresponding to each X value in the table. Write the Y value and its sign (+ or -) calculated in the cell below its X value. Pick any three of the X values and on a separate worksheet, show how you calculated its Y value. Use these X,Y pairs also if you chose to do the bonus option. Find the critical values among the given X values…
- The function C(x)=−24x+1936 represents the cost to produce x items. What is the least number of items that can be produced so that the average cost is no more than $20?Does the output maximization level of input use exist for the following function? If yes, then what is the exact input-use level? y = x1 + 0.1x12 - 0.05x13 + x2 + 0.1x22 - 0.05x23Which ONE of the following descriptions is CORRECT according to this Normal Form?
- A manufacturer of a new patented product has found that he can sell 70 units a week to the customer if the price is $48. In error, the price was recently advertised at $78 and as a result, only 40 units were sold in a week. The manufacturers fixed costs of production are $1,710 a week and variable costs are $9 per unit. You are required to: d. Assuming a sudden change in trading conditions resulting in a 20% reduction in demand at all price levels, to find the equation of the new demand function and to recommend how the manufacturer should respond.A retail store in Makkah, receives shipments of a particular product from Jeddah and Taif. Let X be units of product received from Jeddah and Y be units of product received from Taif.a. Write an expression for the total units of product received by the retail store in Makkah. b. Shipments from Jeddah cost $0.20 per unit, and shipments from Taif cost $0.25 per unit. Develop an objective function representing the total cost of shipments to Makkah.c. Assuming the monthly demand at the retail store is 5000 units, develop a constraint that requires 5000 units to be shipped to Makkah. d. No more than 4000 units can be shipped from Jeddah and no more than 3000 units can be shipped from Taif in a month. Develop constraints to model this situation.e. Of course, negative amounts cannot be shipped. Combine the objective function and constraints developed to state a mathematical model for satisfying the demand at the Makkah retail store at minimum cost.Evaluate the integral. (Use C for the constant of integration.)