I am given this question: The price p, in dollars, of a certain commodity and the quantity x sold obey the demand equation p = (−x/5)+200 where 0 ≤ x ≤ 1000 Suppose that the cost C, in dollars, of producing x units is C =(√x/10)+400. Assuming that all items produced are sold, find the cost C as a function of the price p. Is it safe to assume that this question has an issue since the cost C cannot be integrated into the price equation?
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I am given this question:
The price p, in dollars, of a certain commodity and the quantity x sold obey the demand equation p = (−x/5)+200 where 0 ≤ x ≤ 1000
Suppose that the cost C, in dollars, of producing x units is C =(√x/10)+400.
Assuming that all items produced are sold, find the cost C as a function of the price p.
Is it safe to assume that this question has an issue since the cost C cannot be integrated into the price equation?
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- The function D(p)D(p) gives the number of items that will be demanded when the price is p. The production cost, C(x)C(x) is the cost of producing x items. To determine the cost of production when the price is $8, you would: A.Solve D(C(x))=8D(C(x))=8 B.Evaluate C(D(8))C(D(8)) C.Evaluate D(C(8))D(C(8)) D.Solve C(D(p))=8Find the price-demand equation for tickets to a particular zoo when the demand is 225 tickets per day at $15.00 per ticket, given that the marginal price-demand function, p′(x), for x number of tickets per day, is given as p′(x)=−0.015e−0.01x. If the zoo only sells 150 tickets per day, what should the price be? Do not round until the end. Round your answer to the nearest hundredth and do not include a dollar sign in your answer.The estimated monthly U.S. demand function for avocados isQ = 144 − 40p + 20pt where p is the price of avocados and pt is the price of tomatoes, a substitute for avocados. The estmated supply function is Q = 58 + 15p − 20pf where the price of fertilizer, pf , is $0.40, so the supply function can be written asQ = 50 + 15p. The initial price of tomatoes is $0.80 per lb. Using algebra, determine the initial equilibrium price and quantity of avocados, and then determine how price and quantity change if the price of tomatoes increases by $0.55 to $1.35
- A manufacturing business can supply 60 plasma TV sets per month at a price of $280 per set, or sell 140 plasma TV sets if the price is $370 per set. A group of retailers will buy 80 plasma TV’s if the price is $350 per pair and 120 plasma TV’s if the price is $300 per set. Given that the demand and supply functions must be linear: Find the linear equations representing both demand and supply Find the point of market equilibrium (number of TVs: q) and the price per unit (p) at that point.You and your friends love to go fishing. There is a sporting goods store in your neighborhood that sells a fishing pole for $82 but costs the store $60, and a fully stocked tackle box that sells for $58 but costs $40. Assuming the mark-up policy is linear, determine the equation that relates price (P) to cost (C). Following this same mark-up policy for other items, what would be the price of a pair of waders which cost the company $80?Use the following general linear supply function: Qs = 40 + 6P - 8PI + 10F where Qs is the quantity supplied of the good, P is the price of the good, PI is the price of an input, and F is the number of firms producing the good.If PI = $20 and F = 60 what is the equation of the supply function?Group of answer choices Qs = 480 + 6P Qs = 40 + 8P P = 480 + 6Qs Qs = 400 + 6P none of the above
- Suppose the estimated supply function for avocados is given by QS = 48 + 15p – 10pf , where pf is the price of fertilizer. The estimated demand for avocados is given by Qd = 233 - 40p + 5pt , where pt is the price of tomatoes per pound. Solve for the initial equilibrium price and quantity of avocados if the price of fertilizer, pf ,is equal to $0.35 per lb. and price of tomatoes, pt, is equal to $0.80 per lb. Solve for the new equilibrium price and quantity of avocados if the price of fertilizer, pf , increases to $0.90 per lb. and price of tomatoes, pt, remains $0.80 per lb. Use these equilibrium values from parts a. and b. to solve for the price elasticity of demand for avocados. Given your calculations, are avocados elastic, inelastic or unit-elastic? Have total expenditures on avocados increased, decreased, or not changed as a result of the change in the price of fertilizer?A toy company is trying to determine the optimal price for their weekly supply to meet the demand for a toy they are about to release. They estimate that the supply function follows p= 0.006q^2 + 0.14q+ 8.62 and the demand function follows p= -1.25q+ 65 , where p is the price of the toy (in dollars) and q is the weekly quantity of the toy (in hundreds). If the company tries to sell the toy for $24, will there be a shortage or surplus of toys each week?Predicting Changes in Equilibrium Price and Quantity Suppose that the market demand for farmed salmon is Qd = 12 – p and the market supply of farmed salmon is Qs = 9.6 + 0.5p – 0.2pt, where Q is the quantity of salmon in millions of tons per year, p is the price of salmon in dollars per pound, and pt is the price of tilapia in dollars per pound. The supply function demonstrates that the facilities that are used to farm salmon are also suitable for farming tilapia. a) Use a market diagram to demonstrate that the equilibrium price and quantity of salmon is implicitly a function of the price of tilapia. That is, show how a change in the price of tilapia will impact the market for farmed salmon. (No need to use numbers here, just sketch and explain.) b) Using the supply and demand functions, derive the relationship between the price of tilapia and the equilibrium price and quantity of salmon. You should ultimately calculate and . Check your work by calculating the impact of an increase in…
- The demand for monorail service in a city in 2005 can be approximated by q = −4,500p + 41,700 rides per day when the fare was $p. Find the function R for total daily revenue in dollars, in terms of p only, subject to any constraints. R(p) = Find R′(p). R′(p) = What price (in dollars) should have been charged to maximize total daily revenue? (Round your answer to the nearest cent.) p = $Consider the supply function: Qs = 60 + 5P – 12 PI + 10F , Where Qs = quantity supplied, P = price of the commodity, PI = price of a key input in the production process, and F = number of firms producing the commodity. (a)Derive the equation for the supply function when PI =$90 and F = 20. (b) Using the supply function from part (a), calculate the quantity supplied when the price of the commodity is $300 and $500. (c)Derive the inverse of the supply function in part (a). using the inverse supply function; calculate the supply price for 680 units of the commodity. Give an interpretation of the supply price.The marketing department of a business has determined that the demand for a product can be modeled by p=2000−10x, where p is the price per unit (in dollars) and x is the number of units. The cost (in dollars) of a producing x units is given by C=2000+500x. What price will yield a maximum profit?