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- A company determines that its weekly profit from manufacturing and selling x units of a certain item is given by Px=-x3+3x2+2880x-500. Use a graphing utility to find the weekly production rate that will maximize the profit.The graph below shows a company's estimated profits (in dollars) for different advertising expenses (in tens of thousands of dollars). The company's actual profit was $988,608.55 for an advertising expense of $290,000. P 1 100 000 900 000 700 000 500 000 300 000 100 000 - 100 000 (29, 988608.55) 5 10 15 20 25 30 35 (b) The company's model is X i (a) From the graph, it appears that the company could have obtained the same profit for a lesser advertising expense. Use the graph to estimate this expense (in dollars). An advertising expense of $ when x = 0 also appears to yield a profit of about $988,608.55. P = 140.75x³ + 5348.3x2 - 76,560, 0 ≤ x ≤ 35 where P is the profit (in dollars) and x is the advertising expense (in tens of thousands of dollars). Explain how you could verify the lesser expense from part (a) algebraically. To verify, evaluate P(x) at x =The cost of a telephone call from Mendocino to San Francisco during business hours is 40 cents for the first minute and 30 cents for each additional minute or fractional part thereof.. Find a mathematical model expressing the cost of a telephone call, lasting not more than 5 minutes, as a function of the duration of the duration of the call. The cost of a telephone call from Mendocino to San Francisco during business hours is 40 cents for the first minute and 30 cents for each additional minute or fractional part thereof.. Find a mathematical model expressing the cost of a telephone call, lasting not more than 5 minutes, as a function of the duration of the duration of the call. The cost of a telephone call from Mendocino to San Francisco during business hours is 40 cents for the first minute and 30 cents for each additional minute or fractional part thereof.. Find a mathematical model expressing the cost of a telephone call, lasting not more than 5 minutes, as a function of the…
- What is the profit function?The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells small radios. How many radios must be produced and sold for the company to break even?The graph shows the exports of iron-ore from country X from January 2001 to December 2001. Thousand tons 800 700 600 500 400 13:00 200 Jan Feb Mar Apr May Jun Ju Exports (Thousand tons) Aug Sep Oct Nov --Exports (Million $) What is the average price, in dollars, per ton of iron-ore in December? (A) $6.15 (B) $61.53 (C) $615.38 (D) $6,153.80 $61,538.00 400 (A) (B) (C) (D) 350 300 250 200 150 100 SO 0 Million $ W What was the approximate maximum price of iron-ore per ton in any of the months? $600 8640 $800 $1,060 $2,000
- The graphs of a company's total revenue function and total cost function are shown. Use the graphs to answer the following questions. $ Dollars R(x) 40,000 f C(x) 20,000 200 400 600 800 Units X (a) From the sale of 100 items, 450 items, and 720 items, rank from smallest to largest the amount of profit received. 100 items, 450 items, 720 items 100 items, 720 items, 450 items 450 items, 100 items, 720 items 450 items, 720 items, 100 items 720 items, 100 items, 450 items 720 items, 450 items, 100 items Explain how to determine the amount of profit received for these items. The profit is found by subtracting the cost from the revenue at each point. The profit is found by adding the cost and the revenue at each pointA record company has determined that the cost of producing CDs is $0.06 per CD plus $597.60 per month in fixed costs. The record company sells each CD for $15. Step 3 of 4: Find the profit function.Suppose an investor purchased x ounces of gold in January 2006 at the prevailing price of $549.86 per ounce and then sold this amount of gold in January 2010 for $1112.30 per ounce. (a) Find an equation to express the realized gain, y, in terms of x. (b) Find the point of intersection of the graph of this equation with the graph y= 10,000 to determine the number of ounces of gold that would result in a gain of $10,000
- 2000 -100 -80 -60 -40 -20 20 40 60 80 100 -2000 2000 + 20 40 60 80 100 -100 -80 -60 -40 -20 -2000 2000 +++ ++ -100 -80 -60 -40 -20 ++ 20 40 60 80 100 ++Suppose that a company has just purchased a new computer for $2400. The company chooses to depreciate using the straight-line method for 4 years? (a) Write a linear function that expresses the book value V of the computer as a function of its age x. (b) What is the domain of the function found in part (a)? (c) Graph the linear function. (d) What is the book value of the computer after 2 years? (e) When will the computer have a book value of $600?Suppose that a company has just purchased a new computer for $4000. The company chooses to depreciate using the straight-line method for 5 years. (a) Write a linear function that expresses the book value V of the computer as a function of its age x. (b) What is the domain of the function found in part (a)? (c) Graph the linear function. (d) What is the book value of the computer after 2 years? (e) When will the computer have a book value of $3200?