In the log-log transformation lecture, we analyzed the price of pet food can. The final model was Ln of Sales Volume = 11.05-2.44 Ln price (where Ln is the natural log) What would the optimal price that maximizes the estimated profit, when the cost is 0.61? (Round up to 2 decimal places)
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- A company produces two different versions of a certain product. Let q₁ indicate the amount produced of the first version. The cost function c(q₁) for the first version (expressed in euros) can be described by the equation c(q₁) = 9₁ · √√0.59² +59₁ 10 a) For which value(s) of q₁ is the instantaneous rate of change of the cost function equal to 1.75? You may use the graphical calculator to find zeros of a polynomial function if needed. b) Using the result from a), give a precise economic meaning for the instantaneous rate of change of 1.75. We now denote 92 as the amount produced of the second version. The equation of the cost function c(9₂) for the second version is unknown. We do know that the current cost for a production of 2 units of the second version is 50 monetary units and that the elasticity of the cost in terms of the produced amount when 92 = 2 is equal to 1.88. c) Give a linear approximation ƒ of the cost function c(9₂) for production amounts close to q₂ = 2.The total cost (in hundreds of dollars) of producing x calculators per day is given by the equation. 20- 15- 10- C(x) = 6 + /2x + 32 Osx< 50 Perform the following calculations and interpret the results. 10 20 30 40 50 Production C'(x) =U %D Cost (hundred dollars)A company has established that the relationship between the sales price for one of its products and the quantity sold per month is approximately p = 78 – 0.11D units. The fixed cost is $800 per month and the variable cost $32 per unit produced. What number of units, D*,should be produced per month and sold to maximize the profit per month related to the product? Round your answer to 2 decimal places.
- A recent engineering was given the job of determining the best production rate for a new type of casting in a foundry. After experimenting with many combinations of hourly production rates and total production cost per hour, he summarized his findings in table below (column 2). The engineering then talked to the firm’s marketing specialist, who provided estimates of selling price per casting as a function of production output (see table 1 column 3). There are 8,760 hours in a year. What production rate would you recommend to maximize total profits per year? a) 100 ; b) 200 ; c) 300 ; d) 400 ; e) 500 show the computation how to solve it.A recent engineering was given the job of determining the best production rate for a new type of casting in a foundry. After experimenting with many combinations of hourly production rates and total production cost per hour, he summarized his findings in table below (column 2). The engineering then talked to the firm’s marketing specialist, who provided estimates of selling price per casting as a function of production output (see table 1 column 3). There are 8,760 hours in a year. What production rate would you recommend to maximize total profits per year? a) 100 ; b) 200 ; c) 300 ; d) 400 ; e) 500 Show handwritten solutions.A large company in the communication and publishing industry has quantified the relationship between the price of one of its products and the demand for this product as Price=160−0.02×Demand for an annual printing of this particular product. The fixed costs per year (i.e., per printing)=$47,000 and the variable cost per unit=$40. What is the maximum profit that can be achieved? What is the unit price at this point of optimal demand? Demand is not expected to be more than 4,000 units per year. The maximum profit that can be achieved is $? (Round to the nearest dollar.) The unit price at the point of optimal demand is $? per unit.
- Company XYZ projects their revenues for the given quarter to be modeled by the function R(z) = 12z - 6z + 2000, where x represents the number of goods sold and R(x) the price. The fixed costs for Company XYZ include rent and wages, and is a total of 10000 each month and the variable costs for the quarter can be modeled by the function V (2) = 12x + 1000. (a) Find the break-even point for Company XYZ. [ Select) (b) Find the marginal profit function. I Select ]For the following problem, what would be the objective function that aims at minimizing the total cost considering that X1, X2, X3, and X4 are the number of units produced and sold of Products 1, 2, 3, and 4, respectively? Manufacturing time (hr) per unit Machine Cost per hr ($) Product 1 Product 2 Product 3 Product 4 Capacity (hr). 10 2 4 2 500 5 3 1 2 380 4 7 1 450 Unit selling price ($) 75 45 O a. 20X1+30X2+40X3+20X4 O b. None of the answers OC. 75X1+70X2+55X3+45X4 Od. 63X1+52X2+53X3+34X4 123 دي دا فيا 70 2 55A manufacturer of handcrafted wine racks has determined that the cost to produce x units per month is given by C= 0.2x +10,000. How fast is the cost per month changing when production is changing at the rate of 18 units per month and the production level is 60 units? Costs are increasing at the rate of $ per month at this production level. (Round to needed.) increasing decreasing
- The Retread Tire Company recaps tires. The fixed annual cost of the recapping operation is $60,000. The variable cost of recapping a tire is $9. The company charges $25 to recap a tire. For an annual volume of 12,000 tires, determine the total cost, total revenue, and profit. Determine the annual break-even volume for the Retread Tire Company operation. Graphically illustrate the break-even point using a one way table that relates volume to profit.A company produces and sells a consumer product and is able to control the demand by varying the selling price. The approximate relationship between price and demand is 2700 5000 p = 38 + (for D>1) D² The company is seeking to maximize its profit. The fixed cost is $1,000 and the variable cost is $ 40 per unit. What is the number of units and total amount that should be produced and sold each month to maximize profit?a) Determine the variable cost per unit and the fixed cost using the high-low method.b) What is the equation of the total mixed cost function?c) Prepare the scatter diagram and insert the trendline or line of best-fit. Use a scaleof 2 cm to represent 1,000 units on the x-axis & 2 cm to represent $50,000 on the yaxis.