The marginal profit for a certain company is MP₁(x)= x² + 18x-45. The company expects the daily production level to rise from x = 3 to x = 5 units. The management is considering a plan that would have the effect of changing the marginal profit to MP₂(x) = -x² +14x-33. Should the company adopt the plan? Determine the area between the graphs of the two marginal profit functions from x = 3 to x = 5. Interpret this area in economic terms. Should the company adopt the plan that would make the marginal profit be MP₂? OA. Yes, because the company will make a larger profit under the new plan. B. No, because the company's profit will be smaller under the new plan. OC. It is impossible to tell using the given information. The area between the graphs of the two marginal profit functions from x = 3 to x = 5 is sq. units.
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- You are an accountant for a manufacturer of radios. The demand function for the tablets is p= 40– 4x² where x is the number of tablets produced in millions. It costs the company $15 to make a tablet. (i). Write an equation for the manufacturer's profit as a function of the number of tablets produced. (ii). The company currently produces 1 million tablets and makes a profit of $21,000,000, but you would like to scale up production a bit. What greater number of tablets could the company produce to yield the same profit?You are an accountant for a manufacturer of radios. The demand function for the tablets is p = 40 – 4x2 where x is the number of tablets produced in millions. It costs the company $15 to make a tablet. (i). Write an equation for the manufacturer’s profit as a function of the number of tablets produced.The variable x represents the number of HDTVs manufactured and sold in a given month. The variable p is the price charged when you sell a TV. A demand curve is given by p = 660-3x. a) Find the x-intercept of this demand curve. Say what it means. Assume you must pay salaries totalling 8000$ in a month. Also, it costs $110 to manufacture one TV. b) Write a formula for your cost function C(x) c) Write a formula for your revenue function R(x) d) The profit function is M(x) = Graph the profit function and using the Maximum program, find the maximum possible profit and fill in the details (round off x to the nearest whole number): e) number of sales: f) profit: g) selling price: h) revenue: i) cost: j) check these results fit together: k) Find the range of prices you can charge and still be in the black: The lowest price you can charge is ___________ and the highest is ___________
- The demand function for a tablet is given by the model P= 200-16x2 where p is measured in dollars per tablet and x is measured in millions of tablets. If it costs $50 to produce each tablet and a profit of $125 million was derive when 2.5 million tablets were produced. Derive the number of tablets that the company could sell to make the same amount of profit?The total cost and the total revenue (in dollars) for the production and sale of x ski jackets are given by C(x) = 28x + 20,160 and R(x) = 200x - 0.2x2 for 0sxs 1000. Find the value of x where the graph of R(x) has a horizontal tangent line. Find the profit function P(x). Find the value of x where the graph of P(x) has a horizontal tangent line. Graph C(x), R(x), and P(x) on the same coordinate system for 0 sxs 1000. Find the break-even points. Find the x-intercepts of the graph of P(x).A community bird-watching society makes and sells simple bird feeders to raise money for its conservation activities. The materials for each feeder cost $5, and the society sells an average of 24 per week at a price of $9 each. The society has been considering raising the price, so it conducts a survey and finds that for every dollar increase, it loses 3 sales per week. (a) Find a function that models weekly profit in terms of price per feeder. (Let x represent the price per feeder and P represent the profit.) P(x) = (b) What price should the society charge for each feeder to maximize profits? $ What is the maximum weekly profit? $
- Suppose that the Travnikar Corporation manufactures widgets. Analysts that work for the company have found a function C(x) which reports the cost to produce x widgets and a function R(x) which reports the total revenue from selling x widgets. Currently, the company is producing 500 widgets, but the analysts find that R'(500)=85 and C'(500)=79. In order to maximize profits, should the analysts recommend increasing or decreasing production?When the admission price for a baseball game was $4 per ticket, 50,000 tickets were sold. When the price was raised to $5, only 45,000 tickets were sold. Assume that the demand function is linear and that the variable and fixed costs for the ball park owners are $0.10 and $95,000 respectively. (a) Find the profit P as a function of x, the number of tickets sold. P(x) = (b) Select the graph of P. y 150000 y 150000 150 000 100 000 100 000 100 000 50 000 50 000 50 000 20000 40 000 60 00p 20000 40 000 60 000 20000 40 000 60 000 - 50 000 -50 000 -50 000 -100 000 100000 100000 The xy-coordinate plane is given. The curve starts at the approximate point (0, 3,000), goes up and right becoming less steep, and exits the window at the approximate point o-150000 O o-150000L O O (70,000, 69,000). 150000 100 000. 50 000- 20000 40 000 60 do0 - 50 000 100 000- o 150 000Find the demand function for the marginal function below. Recall that if no items are sold, the revenue is $0. R'(x) = 0.03x2-0.08x + 196
- Use the functions given below to solve the problem. C(x) represents the cost, in dollars, of x units of a product and R(x) represents the revenue, in dollars, from the sale of x units. Find the number of units that must be produced and sold in order to break even, C(x) = 72,000 + 43x and R(x) = 47x The number of units that must be produced and sold in order to break even is units.The profit from the supply of a certain commodity is modeled as P(q) = 71ge-0.29 dollars where q is the number of units produced. 0 ≤ q ≤ 100 (a) Write an expression for the rate of change of profit. (Be sure to use q as the independent variable.) P'(q) dollars per unit (b) At what production level in the domain 0 ≤ q ≤ 100 is the rate of change of profit zero? (Round your answer to the nearest whole number.) q= units (c) What is profit at the production level found in part (b)? (Round your answer to two decimal places.)You have been hired by Kia as manager for its Pakistan operations. Assume following is the short-run production function at their assembly plant outside Karachi: Q = 10L2 – 0.5 L3 where L is variable input labor, Q is output of Cars assembled Find the ranges of the three stages of production. Demonstrate the relationship between Total Production, Marginal Product and Average Product in a hypothetical graph and clearly label the three stages as per the values of Lyou observed in (a) above At the end of the year it is expected that output will double with purchase ofnew equipment and machinery. The production function is estimated to be Q = 60L.30K.70 where L is labor and K is capital. Suppose initial L1 = 1 and K1 = 1. When inputs are in increased to L2 = 2 and K2 = 2, do you observe increasing, decreasing or constant returns to scale? Assume Kia Head Office is considering hiring more laborers either at their Gwadarplant or alternatively…