What combination of goods x and y should a firm produce to minimize costs when the cost function is C(x, y) = 6x² + 10y? – xy + 30 and the firm is subject to the production quota of x + y = 34? What is the minimum cost for the firm?
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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?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?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))=8
- 1.The price p in dollars of a certain commodity and the quantity x sold obey the demand equation p= -1/5x + 200 where 0<=x <=1000. Suppose that the cost C in dollars of producing x units is C= the square root of x divided by 10 + 400. Assuming that all items produced are sold, find the cost of c as a function of the price p.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?The demand function for a good is given by the equation P = a-bQ while the total cost function is TC = Dq2 + eQ + f, Where a,b,c,d,e and f and positive constants. 1. Derive the equation for profit. 2. Derive an expression for the value of Q for which profit is maximized.
- The demand function for x is D(p) = 65 - 2p and the supply function is S(p) = 20 + p. What is the price that should be set to restrict the quantity supplied to 30 units?The demand equation of a certain product is p=90-q-q². The total cost function is c=50+q-0.1q². Find the profit function. Simplify your answer as much as possible.A firm orders 12, 30 and 25 items of goods G1, G2 and G3. The cost of each item of G1, G2 and G3 is $8, $30 and $15, respectively.(a) Write down suitable price and quantity vectors, and use matrix multiplication to work out the total cost of the order.(b) Write down the new price vector when the cost of G1 rises by 20%, the cost of G2 falls by 10% and the cost of G3 is unaltered. Use matrix multiplication to work out the new cost of the order and hence find the overall percentage change in total cost.
- 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.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 $1.35A manufacturer of upholstery can sell 2121 yards of fabric at a price of $3.11$3.11 per yard. If the price is $1.85$1.85, she can sell 3535 yards. The total cost of manufacturing x yards of fabric is C(x)=0.6x+36C(x)=0.6x+36 dollars. Step 1 of 3 : Assuming the demand function is linear, find an equation for D(x)D(x). Do not round your answer.