A manufacturer can sell x number of units of its products produced per day át a priCe o (35 – 0.10x) pesos. It costs P25 to produce each unit of the product. The fixed cost is 500. a. Formulate the TR, TC, and Profit function. b. Determine the production level that will yield maximum profit. How much would be the maximum profit? C.
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- XYZ Enterprises produce slippers in 10 different designs. It takes one hour (and PhP20,000) to set up between designs and, after setting up, they can produce 1,000 units of a particular design per hour (at a cost of PhP9,000). Does this production exhibit scale economies or scope economies?Rex Carr owns a junkyard which processes used cars into scrap metal. In the long-run Rex can use two methods to destroy cars. The first involves purchasing a hydraulic car smasher which costs $200 a year to own and then spending $1 for every car smashed. The second method involves purchasing a hammer that will last one year and costs $40, and paying his brother Otto Carr to destroy the cars at a cost of $5 each. What is the minimum number of cars processed per year for which Rex should be willing to purchase the hydraulic smasher?(You will need to use a spreadsheet to tackle these questions.) 1. How much of q can be produced for £60,000 if the total cost function is TC = 86 + 152q − 12q2 + 0.6q3? 2. What output can be produced for £150,000 if TC = 130 + 62q − 3.5q2 + 0.15q3? 3. Solve for x when 0 = −1,340 + 14x + 2x2 − 1.5x3 + 0.2x4 + 0.005x5 − 0.0002x6
- The profit function in dollars for a product is given -x^3+76x^2-380x-2800 where x is the number of units produced and sold. If break even occurs when 10 units are produced and sold find a quadratic factor of the profit function and find a number of units other than 10 that gives break even for the product.It is known that a certain company sells each kg of the product it manufactures at $80, it is also known that the total manufacturing cost "CT" is given by the function CT=(1/1000)x2 +100 , where "x" are the kg of product produced. a) How many units of "x" must the company sell to break even? Value = 100 points.b) How many units of "x" is the optimal quantity that should be sold to optimize the producer's profit? Value = 100 points.c) How many monetary units does that optimal profit for producers amount to? (remember, you will have to prove it mathematically either by the method of the first or by the method of the second derivative). Value = 100 points.Worldwide annual sales of a device in 2012–2013 were approximately q = −6p + 3,040 million units at a selling price of $p per unit. Assume a manufacturing cost of $40 per unit. [HINT: Recall that Profit = Revenue − Cost.] Find the function P for annual profit, in millions of dollars and in terms of p only, subject to any constraints. P(p) = ____ Find P′(p). P′(p) = ____ What selling price (in dollars) would have resulted in the largest annual profit? (Round your answer to two decimal places.) p = $____ What would have been the resulting annual profit (in millions of dollars)? (Round your answer to the nearest whole number.) $ ____ million
- Jim has been employed at Gold Key Realty at a salary of $2,000 per month during the past year. Because Jim is considered to be a top salesman, the manager of Gold key is offering him one of three salary plans for the next year: (1) a 25% raise to $2,500 per month; (2) a base salary of $1,000 plus $600 per house sold; or, (3) a straight commission of $1,000 per house sold. Over the past year, Jim has sold up to 6 homes in a month. Write down the month salary payoff table for Jim.A small bank is trying to determine the number of tellers to employ. The total cost of employing a teller is $100 per day, and a teller can serve an average of 160 customers per day. On average, 210 customers arrive per day at the bank, and both service times and interarrival times are exponentially distributed. If the delay cost per customer day is $200, how many tellers should the bank hire?A manufacturer estimates that its product can be produced at a total cost of c(x)=40,000+100x+x^3 dollars. If the manufacturer's total revenue from the sale of x units is R(x)=4300x dollars, determine the level of production x that will maximize the profit. Find the maximum profit.
- Complete all of the following definitionsA copy company wants to expand production. It currently has 20 workers who share eight copiers. Two months ago, the firm added two copiers, and output increased by 60,000 pages per day. One month ago, the firm added five workers, and productivity also increased by 25,000 pages per day. A copier costs about three times as much as a worker. Assume these increases in productivity per worker and productivity per copier are good proxies for future increases in productivity when hiring additional workers or purchasing additional copiers. Based on this information, the copy company should hire another worker or purchase another copier in order to expand output.If the fixed cost of producing output Y is P150,000, variable cost is P300 per unit and the price of Y is P600 per unit. How many units should be produced to break-even?