Consider the following quadratic (potential cost) function: c(w, y) = [/₁1wi +√22w² +2/12w1/²w2/2]y, where ₁,W2 and y are input prices and output, respectively, and a, 711, 722; 12 are parameters. Which restrictions hould the parameters satisfy in order for this function to be: (i) homogeneous of degree one in prices (ii) prigon?
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Consider the following quadratic (potential cost) function
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- 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 $? per unit. A lash adjuster keeps pressure constant on engine valves, thereby increasing fuel efficiency in automobile engines. The relationship between price (p) and monthly demand (D) for lash adjusters made by the Wicks Company is given by this equation D (1.900-py0 10 What is the demand (0) when total revenue is maximized? What important data are needed if maximum profit is desired? G The total revenue is maximized when demand is 9500 units per month (Round to the nearest whole number) Select all important data that are needed if maximum profit is desired. DA Variable cost per lash adjuster B. Fixed cost per month C. Variable cost per engine valve D. Variable cost per gallon of fuelQ1. Game console manufacturing determines that in order to sell Q units, the price per unit (in dollar) must decreased by the linear demand (the demand function) P(Q)= 800- 0.3Q($/device) The manufacturer also determine that the cost depends on the volume of production and includes a fixed part 500,000($) and a variable part 500Q , that is C(Q)= 500000+ 500Q What price per unit must be charged to get the maximum profit?
- 1) a) Solve the following inequalities:(i) 5(11 − ?) < ? + 49 (ii) 7? − 3 <10m + 23< 8 − 5m (iii) ?2 ≥ 15 − 2? b) The cost structure for iPhones are as follows, fixed cost of $25 and variable cost perunit of $2. The associated demand function isp = 20 − q .(i) Obtain an expression for the profit, π(q). (ii) Find the range of output which gives a profit of at least $31. c) Use Microsoft Word or Excel to solve the system of linear inequalities:r + 5t ≤ 57t – 2r ≤ 4 r ≥ 0(NB: clearly identify the solution set by placing a BIG enough ‘S’ to coverthat entire region).2. A company supplies a product at two mutually exclusive (do not happen at the same time) periods of time. The demand function for Period 1 is P₁ = 800-20₁ and the demand function for Period 2 is given by P₂ = 760-202. The cost for each unit provided is 40 per unit (paid in both markets). Capacity costs 60 per unit and is only paid once and used in both periods. Find the optimal (maximum) profit.= 2. The cost of operating a jet-powered commercial (passenger- carrying) airplane varies as the three-halves (3/2) power of its velocity; specifically, Co kny3/2, where n is the trip length in miles, k is a constant of proportionality, and vis velocity in miles per hour. It is known that at 400 miles per hour, the average cost of operation is $300 per mile. The company that owns the aircraft wants to minimize the cost of operation, but that cost must be balanced against the cost of the passengers' time (CC), which has been set at $300,000 per hour. At what velocity should the trip be planned to minimize the total cost, which is the sum of the cost of operating the airplane and the cost of passengers' time?
- Acrosonic's production department estimates that the total cost (In dollars) Incurred in manufacturing x ElectroStat speaker systems in the first year of production will be represented by the following function, where R(x) is the revenue function in dollars and x denotes the quantity demanded. Find the following functions (in dollars) and compute the values (in dollars). C(x) - 290x + 18,000 and R(x) - -0.04x + 800x (a) Find the profit function P. P(x) = (b) Find the marginal profit function P'. P'(x) = (c) Compute the following values. P'(4,000) - P'(10,000) =ABC Company is the manufacturer of a low-noise air-purification system. Its current capacity is 10,000 units/month, but ABC received orders totaling 9,000 units each month. Currently, ABC sells its system at a price of $200 per unit, its fixed cost is $500,000/month, and its variable cost is $100/unit. Note that currently, half of ABC’s variable cost is materials, and the other half is labor cost (wages for workers). ABC wants to consider cutting its price by 10% to stimulate demand. If ABC expands its capacity, it will have to lease additional manufacturing machines, each of which will cost $20,000/month to lease and can add 1000 units to ABC’s capacity. All existing workers are already working full-time. So, if ABC expands production, ABC has to either pay existing employees for overtime (1.5 times the regular wages) or hire new workers, who are expected to be paid 90% of the hourly wage of existing workers but produce only 75% of the hourly output of existing workers. (a) What is…Complete all of the following definitions
- The Nike accounting firm analyzes the price-demand relationship toconclude that x thousand shoes will sell if offered for a unit price (in dollars) of p(x) = 130−0.1x. Suppose further that the total cost of production was tracked to be $530,000 up until production of the first thousand shoes, and that this cost increased linearly to $560,000 by the time of production ofthe 2000th shoe. Find the following quantities, and interpret your results(describe what these quantities represent). a) Marginal revenue when x= 100 b) Average profit when x= 500Given the following TR function, Calculate the exact change in total revenue (ATR=??) as the output (Q) decreases from 5 to 4 units. * TR = 10Q – Q² O 2 O 1.5 -15. You are employed as a research and development manager for a production company. The chief executive officer of the company has asked you to generate costing data to better assist in expansionaryplanning for the company. You are required to generate costs data from the equation below. C(y) = 23y2 + 12y + 8 assume 10 < y ≤ 30Calculate each cost for (a)-(f) in terms of $ values based on your selected (y) and provide a graphical representation of all cost curves from (a)-(f) on one graph. Please note that the graph need not to be drawn to scale but all curves should be labeled clearly.(a) variable costs;(b) fixed costs;(c) average variable costs;(d) average fixed costs;(e) average total cost;(f) marginal costs. 6. Optimize the Cobb-Douglas production function given the following parameters. The maximum about of money available to spend is $1, 600 where the price of K = 12 and the price of L = 6. That is Pk = 12 and Pl = 6. The function is given as q = K0.4L0.6. Using the Lagrangian…