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QH: Use the demand function D(p)=(p-10)^2 * (p+10)^2 for p values between 0 and 10. Suppose there is no per-item cost. What is the optimal price to set? Calculus (derivatives) won’t be much help here. Figure out a way to do it using technology (desmos? Wolfram alpha? Trying different numbers? spreadsheet?).
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- a = F + 0, B = S + 4 Q = T + 1. By using these values of a, B, and Q, Solve al| questions of the following questions. Consider %3D %3D %3DA bookstore purchased a best selling book at P200 per copy. At what price should this book be sold so that, giving a 20% discount, the profit is 30%.Suppose that the manufacturer of a gas clothes dryer has found that when the unit price is p dollars, the revenue R (in dollars) is R(p) = -5p² + 10,000p. (a) At what prices p is revenue zero? (b) For what range of prices will revenue exceed $1,500,000? (a) At what prices p is revenue zero? The revenue equals zero when p is $ (Use a comma to separate answers, but do not use commas in any individual numbers.) (b) For what range of prices will revenue exceed $1,500,000? (Type your answer in interval notation. Round to the nearest cent as needed.).
- (Marginal Analysis). A retailer has determined that the monthly sales of a watch are 150 units when the price is $50, but decrease to 120 units when the price is $60. Assume that the demand is a linear function of the price. (4a) Find the demand as a linear function of the price (4b) Find the revenue R as a function of x (4c) Approximate the change in revenue for a one-unit increase in sales when x = 141Target buys hand sanitizers from the wholesaler at $3 and sells them in their stores at $8. Find the original markup. Now, assume the hand sanitizers does not sell for $8 so the store has to reduce the price by 10%. Calculate the final selling price and the maintained markup.A cost of production function is given as C (n) = (n – 100)2 + 100 where C (n) is the cost in $ of producing n number of a certain product. Use the derivative to determine the n which will minimize the cost of production. n = 10 n = 100 c) n = 50 d) n = 20
- The manufacturer of Brand A automobile tires claims that its tire can save 120 gallons of fuel over 56,000 miles of driving, as compared to a popular competitor (Brand B). If gasoline costs $3.50 per gallon, how much per mile driven does this tire save the customer (Brand A versus Brand B)? The savings are S per mile (Round to three decimal places)Find the partial derivatives of the following function: (7xz4-5x²z3+3x5)4 (3xz5-2x4+8z3)5 y=f(x,z) = (3xz5– 2xª + 8z354(7xzª – 5x²,3+ 3x5^(7z4– 10xz³+15x4 – (7xzª- 5x²,3+3x545(3xz5_- 2xª+ 8z35{3z 5-8x3 [(3xz- 2x4+ 8z 35,2 fx = - 2x+ 8z I. (3xz5- 2x+ 8z 354(7xzª – 5x²z3+ 3x5³(28xz3 – 15xz3- (7xz4- 5x²23+ 3x 3x545(3xz5- 2xª+ 8z3^(15xzª+16z) 2.3 [(3x25- 2x4+ 8z 35,² (3xz5 – 2x4+ 8z 35(7xz4 – 5x²23+ 3x5³(7z4– 10xz3+15x4– (7xz^- 5x²z3+3x 9(3xz5-2xª+8z3^(3z5-8x3 [(3x2 5- 2x4+ 8z351² O I. (3xz fz '- 2x*+ 8z 3(7xz4_ 4 - 5x2z3+ 3x3(28xz 3-15x223- (7xz4- 5x?z3+ 3x54(3xz5- 2x4+ 8z34(15xz4+16z) [(3x2 5- 2x4+ 82 35j² -2x*+ 8z354(7xzª – 5x²,3+ 3x5³(7zª – 1Oxz3 +15x4 - (7xz^– 5x²½³+ 3x545(3xz5– 2xª+ 8z 34(325- 8x³ + 8z° [(3x25- 2x4+ 8z 35,2 (3xz5- 2x4+ 8z 354(7xz4– 5x²z3+ 3x5%½28xz3-15x?z2+ 3x) - (7xz4- 5xz³+ 3x45(3xz5- 2x+8z34(15xz4 - 2x+16z) (3xz 5- 2x4+ 82 35j² 2.3 - 10xz+15x - 2x+ 8z fx = II. 2_3 fz %3D fx =- (3xz5– 2x* + &z 3}54(7xz* – 5x²z ³ + 3x5³(7z* - 10xz³+15x*) – (7xz*- 5x²z³+ 3x5*5(3xz5–…Let 10p + x = 100 be the demand equation, where p is the price per item when x items are demanded. (a) Find the total revenue when the level of production is: (i) 40; (ii) 41; (b) Find the exact revenue derived from the 41st item. (c) Find the approximate revenue derived from the 41st item. (d) What is the error if the derivative is used to approximate the marginal revenue?
- A construction manager just starting in private practice needs a van to carry crew and equipment. She can lease a used van for $3,777 per year, paid at the beginning of each year, in which case maintenance is provied. Alternatively, she can buy a used van for $5,669 and pay for maintenance herself. She expects to keep the van for three years at which time she could sell it for $1,110. What is the most she should pay for uniform annual maintenance to make it worthwhile to buy the van instead of leasing it, if her MARR is 20%?compute a piece rate for an employee earning $17.75/hour where the standard time per unit is ten (10) minutese(p, v(p, w)) = v(p, w) - ((p1 * w1) + (p2 * w2)) how to map the correct numbers: there four prices one for the inital then ther other ((p1 * w1) + (p2 * w2))