Homework Answers
| number of garden hoses | total revenue | total cost | profit |
| 0 | 0 | 622 | -622 |
| 25 | 500 | 697 | -197 |
| 50 | 896.4466 | 772 | 124.4466 |
| 75 | 1225.481 | 847 | 378.4809 |
| 100 | 1500 | 922 | 578 |
| 125 | 1727.458 | 997 | 730.4575 |
| 150 | 1912.883 | 1072 | 840.8827 |
| 175 | 2059.968 | 1147 | 912.9676 |
| 200 | 2171.573 | 1222 | 949.5729 |
| 225 | 2250 | 1297 | 953 |
| 250 | 2297.153 | 1372 | 925.1529 |
| 275 | 2314.641 | 1447 | 867.6409 |
| 300 | 2303.848 | 1522 | 781.8476 |
| 325 | 2265.979 | 1597 | 668.9792 |
| 350 | 2202.1 | 1672 | 530.0996 |
| 375 | 2113.156 | 1747 | 366.1562 |
| 400 | 2000 | 1822 | 178 |
| 425 | 1863.401 | 1897 | -33.5995 |
| 450 | 1704.058 | 1972 | -267.942 |
| 475 | 1522.615 | 2047 | -524.385 |
| 500 | 1319.66 | 2122 | -802.34 |
| 525 | 1095.739 | 2197 | -1101.26 |
| 550 | 851.3567 | 2272 | -1420.64 |
| 575 | 586.9844 | 2347 | -1760.02 |
| 600 | 303.0615 | 2422 | -2118.94 |
| 625 | 1.64E-11 | 2497 | -2497 |
roots of the equation are +31.5186,+421.205,-26.221
Suppose a company has fixed costs of $54,400 and variable cost per unit of 1/3x +...
Suppose a company has fixed costs of $54,400 and variable cost per unit of 1/3x + 333 dollars, where x is the total number of units produced. Suppose further that the selling price of its product is 2065 - 2/3x dollars per unit. (a) Find the break-even points. (b) Find the maximum revenue. (c) Form the profit function P(x) from the cost and revenue functions. Find maximum profit. (d) What price will maximize the profit
Let x be the number of graphing calculators being made by Texas Instrument. When x =...
Let x be the number of graphing calculators being made by Texas Instrument. When x = 150 calculators are made it costs the company $495 to make them. When x = 280 calculators are made, it costs the company $820 to make them. a) If Cix), the cost function for producing x calculators is a linear function, write C(x) as a linear function of the form C(x) = mx+b. b) P(x), the profit function of dollars for producing x calculators...
14. Suppose that when the price of a certain commodity is p dollars per unit, then...
14. Suppose that when the price of a certain commodity is p dollars per unit, then x hundred units will be purchased by consumers, where = -0.05 x + 38 The cost of producing x hundred units is hundred dollars is C(x) = 0.02x2 + 3x + 574.77 hundred dollars a. Express the profit P obtained from the sale of x hundred units as a function of x. Sketch the graph of the profit function. b. Use the profit curve...
x²+2x+2 4. Let y=f(x)= x² – 3x-5 (a) Find f(3) (b) Find and simplify f(x) -...
x²+2x+2 4. Let y=f(x)= x² – 3x-5 (a) Find f(3) (b) Find and simplify f(x) - $(3) X-3 f(x)- $(3) (c) Find lim X-3 (d) Find and simplify $(3+h)-f(3) h 13 (e) Find lim f(3+h) – S (3) h 0 h (t) Find the slope-intercept form of the tangent line to y = f(x) at x = 3. (g) Plot the curve and the tangent line on the same graph, using the form on the window (-3,7]*[-10,10). 5. A car...
Given the cost function C(a)-5 c 107 and revenue function R (x) 11x, where a is...
Given the cost function C(a)-5 c 107 and revenue function R (x) 11x, where a is the number of units produced, find the value of x for the break-even point. Round up to the next greater whole number, if necessary
(a) The total cost, in millions of dollars, of producing x thousand units of an item...
(a) The total cost, in millions of dollars, of producing x thousand units of an item is C(x) = 4(x - 5)2 + 4. Plot at least 2 points on the function C(x) with x on the horizontal axis. Then click Connect Points. Plot the vertex and 2 additional points. Vertex Point Connect Points Delete Reset Vertex 2 9.3, 20.9 (b) The revenue (in millions of dollars) from selling x thousand units of the item is R (X) = 5x....
3. (20 points]Let x = 5000 - 20p where pe price and 1= demand. (a) Express...
3. (20 points]Let x = 5000 - 20p where pe price and 1= demand. (a) Express the revenue function R(p) in terms of p. (b) Compute for the marginal revenue with the price set at p = 100. (c) With the goal of maximizing the revenue function, determine if we should increase the price when the current price is set at $100/unit. Give your reason. (d) Given the cost function C(x) = 4000+80r and with the price set at $100/unit....
3. A monopolist chooses output (x) to maximize profit (T) where r(x) = p(x)x-c(x) In this...
3. A monopolist chooses output (x) to maximize profit (T) where r(x) = p(x)x-c(x) In this equation, p(x) denotes the price of x and c(x) is the cost of producing x. Since demand curves are downward sloping, we assume that p,(x) <0. In addition, we will assume that marginal cost is positive and non-decreasing; that is, c'(x) > 0 and c"(x) 2 0. Derive a condition on the demand curve such that marginal revenue is downward sloping. Derive the first...
Break-Even Analysis A multimedia company produces DVDs. It estimates their cost function to be: C(x) =...
Break-Even AnalysisA multimedia company produces DVDs. It estimates their cost function to be:C(x)=13.2 x+48,038The DVD is sold to retail outlets and the revenue function is:R(x)=16.61 xBoth C(x) and R(x) are in dollars and x= number of DVDs manufactured and sold.How many DVDs must be manufactured and sold in order for the company to break even? (Round to the nearest whole number).Equilibrium AnalysisSuppose that the demand function and supply function for honey are P=D(q)=-1.3 q+23 andP=S(q)=0.5 q+2.9where P is the price...
Numbers 8, 12, 18, 20 8. Find the equation of the line perpendicular to 3x -...
Numbers 8, 12, 18, 20
8. Find the equation of the line perpendicular to 3x - 4y 12 and passing through (6,1). 9. The annual revenue of a new web-services company in dollars is given by R(n)- 125n, where n represents the number of users the company has registered. The annual maintenance cost of the company's registered user base in dollars is given by the formula C(n) 85n+22, 480 where n represents the users. a. Write a function that models...
Let x be the number of graphing calculators being made by Texas Instrument. When x = 150 calculators are made it costs the company $495 to make them. When x = 280 calculators are made, it costs the company $820 to make them. a) If Cix), the cost function for producing x calculators is a linear function, write C(x) as a linear function of the form C(x) = mx+b. b) P(x), the profit function of dollars for producing x calculators...
14. Suppose that when the price of a certain commodity is p dollars per unit, then x hundred units will be purchased by consumers, where = -0.05 x + 38 The cost of producing x hundred units is hundred dollars is C(x) = 0.02x2 + 3x + 574.77 hundred dollars a. Express the profit P obtained from the sale of x hundred units as a function of x. Sketch the graph of the profit function. b. Use the profit curve...
x²+2x+2 4. Let y=f(x)= x² – 3x-5 (a) Find f(3) (b) Find and simplify f(x) - $(3) X-3 f(x)- $(3) (c) Find lim X-3 (d) Find and simplify $(3+h)-f(3) h 13 (e) Find lim f(3+h) – S (3) h 0 h (t) Find the slope-intercept form of the tangent line to y = f(x) at x = 3. (g) Plot the curve and the tangent line on the same graph, using the form on the window (-3,7]*[-10,10). 5. A car...
Given the cost function C(a)-5 c 107 and revenue function R (x) 11x, where a is the number of units produced, find the value of x for the break-even point. Round up to the next greater whole number, if necessary
(a) The total cost, in millions of dollars, of producing x thousand units of an item is C(x) = 4(x - 5)2 + 4. Plot at least 2 points on the function C(x) with x on the horizontal axis. Then click Connect Points. Plot the vertex and 2 additional points. Vertex Point Connect Points Delete Reset Vertex 2 9.3, 20.9 (b) The revenue (in millions of dollars) from selling x thousand units of the item is R (X) = 5x....
3. (20 points]Let x = 5000 - 20p where pe price and 1= demand. (a) Express the revenue function R(p) in terms of p. (b) Compute for the marginal revenue with the price set at p = 100. (c) With the goal of maximizing the revenue function, determine if we should increase the price when the current price is set at $100/unit. Give your reason. (d) Given the cost function C(x) = 4000+80r and with the price set at $100/unit....
3. A monopolist chooses output (x) to maximize profit (T) where r(x) = p(x)x-c(x) In this equation, p(x) denotes the price of x and c(x) is the cost of producing x. Since demand curves are downward sloping, we assume that p,(x) <0. In addition, we will assume that marginal cost is positive and non-decreasing; that is, c'(x) > 0 and c"(x) 2 0. Derive a condition on the demand curve such that marginal revenue is downward sloping. Derive the first...
Numbers 8, 12, 18, 20
8. Find the equation of the line perpendicular to 3x - 4y 12 and passing through (6,1). 9. The annual revenue of a new web-services company in dollars is given by R(n)- 125n, where n represents the number of users the company has registered. The annual maintenance cost of the company's registered user base in dollars is given by the formula C(n) 85n+22, 480 where n represents the users. a. Write a function that models...
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