The input-output curve of a gas-fired generating unit is approximated by the following function: H(P) = 120 +9.3 P + 0.0025 P² MJ/h This unit has a minimum stable generation of 200 MW and a maximum output of 500 MW. The cost of gas is 1.20 $/MJ. Over a 6-h period, the output of this unit is sold in a market for electrical energy at the prices shown in the table below.
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- = 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?Problem 6Cannes Croissants (not a real company) wishes to determine the optimum production quantity for its topselling product, almond croissants. The annual demandfor almond croissants is 12,000 units. The setup costs fora production run of the croissants is US$15. The holdingcost per unit per year is US$0.50. Production is mostefficient when 80 croissants are produced per day. Thecompany operates 300 days during a year.a What is the economic production quantity (EPQ)?b How many production runs will there by per year?c What is the maximum inventory level?d What is the total annual cost (in US dollars)?e What is the length of a production run in days?show solution An oil refinery produces one base type of crude oil. The total cost is given by the equation Total Cost, TC = 50,000+20.2D +0.0001D2. The sales price in dollars per barrel is 35. At what level of production in barrels/week is cost/barrel minimum? What is the minimum cost per barrel? What is the maximum weekly profit that the company can make? At what level of production is the maximum weekly profit attainable? and Over what range of production is profit possible? Express answers in whole numbers and write the numerical values only.
- What can you say about negative and positive gross margin in sensitivity analysisThe following figure shows the incremental cost of two units and the marginal cost (old) of the system, when all constraints are met. If both units were dispatched at their minimum values, what would be the marginal cost of the new system (new)? Select one: a The incremental cost of unit 1 Ob. Approximately 46.3 $/MWh S/MWh 49 48 C1=45+0.02Pg1 47 46 45 44 C2=43+0.006Pg2 I C. The incremental cost of unit 2 0 100 200 300 400 500- 600 MWA company produces and sells a consumer product and is ableto control the demand by varying the selling price. The approximate relationship between price and demand is p = 38+ (2,700/D) - (5000/D²) for D>1 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 that should be produced and sold each month to maximize profit? A 71 B 60 с 50 D 25
- Lulu hypermarket estimates daily demand of 18 kgs for a product. It costs RO 100 to make and receive an order, and it takes 16 workdays to receive it. The annual holding cost is 25 % of purchase price. The price RO 2 per kg. The company is operating 5 days per week, and a total of 210 workdays in one year. What is the minimum annual total holding and ordering cost in RO? Round-up to the nearest integer O a. 152 O b. None is correct O c. 725 O d. 625 O e. 615A trailer manufactor has multiple products designed to be towed by a pickup (Ford F-150, Toyota Tacoma, etc). The production of one of their products - the XL7 5x10 trailer - referred to as XL7510 here, has a fixed 9 cost of $62,308 and a variable cost per unit of XL7510 equal to 202 + - dollars, where is the total 10 number of XL7510s produced. Suppose further that the selling price of this product is 1118 The x-values of the break-even points are The maximum revenue is Form the profit function: P(x) = = The maximum profit is The price that will maximize profit is 1 - dollars per unit of XL7510. 10 dollars (round to the nearest cent) dollars (round to the nearest cent)If company A manufactures t-shirts and sells them to retailers for US$9.80 each. It has fixed costs of $2625 related to the production of the t-shirts, and the production cost per unit is US$2.30. Company B also manufactures t-shirts and selll them directly to consumers.The demand for its product is p = 15 −x 125, its production cost per unit is US$5.00 and its fixed cost are the same as for company A . (i) Derive the total revenue function, R(x) for company A. (ii) Derive the total cost function, C(x) for company A. (iii) Derive the profit function, Π(x) for company A. (iv) Using a spreadsheet, create a table for showing x, R(x)?, C(x) for company A in the domain x = 50, 100, 150, 200, 250, 300, 350, 400, 450.(v) Graph the functions from (d) above on the same axes. (vi) From your graph, determine the break-even level of output for company A. (vii) Derive the total revenue function, R(x) for company B. (viii) Derive the profit…
- Using the following assumptions calculate the marginal cost of both a simple cycle and combined cycle gas generator: Simple Cycle hear rate (GJ/MWh) 10 Simple Cycle Variable O&M ($/MWh) $3.50 Combined Cycle heat rate (GJ/MWh) 7 Combined Cycle Variable O&M ($/MWh) $5.00 Gas Price ($/GJ) $3.00 Tonnes of CO2 per GJ 0.051 Carbon Price ($/Tonne of CO2) $20.00 a) What is the variable cost of a simple cycle and combined cycle plant? b) What do the differences in variable cost suggest about each technology’s capacity factor? c) What would happen if carbon prices when to $170/tonne? d) How do you think a $170/tonne carbon price would impact electricity prices?Last year, a company introduced a new version of its main product. The product costs $24002400 to develop (i.e. the start up costs) and $3535 to manufacture each product. Do all the following problems on your page: i) Give a linear equation in the form C(n)=mn+bC(n)=mn+b that gives the total cost to produce nn of these products. Give your answer in function notation. No steps or work are required, just give the function. ii) Find the total cost to produce n=3500n=3500 of these products. Show what numbers you used in your arithmetic calculations. Use function notation in your work. Answer in a complete sentence form with units and context. iii) If the company has $5315053150, how many of these items can be produced? Use function notation in your work. Answer in a complete sentence form with units and context.1. A service station uses 2500 oil filters during the course of a year, and this usage is constant throughout the year. These oil filters are purchased from a supplier 100 miles away for $15 each, and the lead time is 2 days. The holding cost per oil filter per year is $1.50 (or 10% of the unit cost) and the ordering cost is $18.75. There are 250 working days per year. a) What is the service station's optimal order quantity and total annual cost of inventory?