Suppose the input combination currently used by a producer is such that the TRS is equal (in absolute value) to the ratio of the input prices. Then, we can conclude that the producer is maximizing her profits. Group of answer choices True False
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- 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. C Should the company adopt the plan that would make the marginal profit be MP₂? O A. 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. O C. 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.C&A Fast Food has four activities in serving a customer: greet customer, take order, process order, and deliver order. Each activity is staffed by one employee (for a total of four employees). The processing time for each activity is given as follows: Greet customer Take order Process order Deliver order Activity Processing time per customer 2 seconds 30 seconds 60 seconds 5 seconds Assume demand is unlimited. If one additional employee is added to the bottleneck activity, what will be the percentage change in process capacity?The total cost function of a firm that produces its product on two assembly lines is given as TC (x,y) = 3x2+6y2-xy The problem facing the firm is to detrmine the least-cost combination of output on assembly lines x and y subject to the side condition that total output equal 20 units. Find the out put of x and y subject to a total of 20 units that minimize total cost by using both substitution and Lagrangian multiplier methods
- (b) A firm manufactures benches and tables: the quantity of benches manufactured is B and the quantity of tables manufactured is T. The total cost of manufacturing benches and tables is given by the equation: Cost = 3B2 + 5T²2 – 2BT. There is a shortage of lumber available to manufacture these items, and so, only 60 items in total have been promised to a customer. (i) Create the Lagrangian expression for Cost. (ii) The Lagrangian equations are given: 6B – 2T – 1 = 0 10T – 2B – A = 0 60 — В - Т%3D0 Calculate the minimum cost possible. (iii) If more lumber now becomes available, what selling price would be required to make a profit on an additional item produced?a) Given that a firm has a production technology, y= (X² + X²)², derive the MRTS12Use 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.
- 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 - 0.05x23A company estimated that the relationship between the unit price and demand per month for a potential new product is approximated by P = $ 100 – $ 0.1D. The company can produce the product by increasing fixed costs $ 17,500 per month, and the estimated variable costs is $ 40 per unit. What is the optimal demand, D*, and based on this demand, should the company produce new product? Why? a) Work out the complete solution by differential calculus, starting with formula for profit or loss per month b) Solve graphically for an approximate answerThe chemical X-2000 is produced using two inputs, benzene (B) and labor (L) in the exact proportions of one gallon of benzene for each two hours of labor services. Firms in the industry have the production function: qX = min[B, 0.5L] The production of X-2000 generates fumes that greatly increase the chance of cancer among workers. The workers would suffer no ill health effects if they were provided with masks containing a filtering system. The masks increase the hourly cost of labor by another $2. Suppose that in response to this health hazard, the government enacts a regulation that requires the firm to provide each worker with a mask. f) Do you think the new regulation will affect the firm’s choice of input levels (i.e. the firm’s cheapest technique) for a given level of output? g) How will the new regulation affect the firm’s total and marginal cost functions?
- For the typical Cobb-Douglas function, q= AKαLβ whereas APL /APK =1 , find out the marginal rate of technical substitution.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? $The variable x represents the number of HDTVs manufactured and sold in a given month. The variable p is the price charged when you sell a TV. A demand curve is given by p = 660-3x. a) Find the x-intercept of this demand curve. Say what it means. Assume you must pay salaries totalling 8000$ 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 ___________