greater than cost. Notice In the graph of the revenue and cost functions that the revenue is greater than the cost between the two break even points. Find the price range for which the company will make a prot by substituting the x-coordinate of each break-even ordered pair into the price-demand equation. ' Substitute x = 68 into the price-demand equation and simplify. p = 0.0016504x2 - 3.2217826x + 1642.649 = 0.0016504(68)2 - 3.2217826(68) + 1642.649 z 1431 Now substitute x = 683 into the price-demand equation and simplify. p = 0.0016504x2 3.2217826x + 1642.649 = 0.0016504(683)2 - 3.2217826(683) + 1642.649 5 212 Thus, the price range for which the company will make a prot is $212 5 p 5 $1431. m (A) Find a quadratic regression equation for the price-demand data, using x as the independent variable. (B)Find a linear regression equation for the cost data, using x as the independent variable. Use this equation to estimate the fixed costs and variable costs per projector. (C)Find the break even points. (D)Find the price range for which the company will make a profit.The table to the right contains pricedemand and total cost data for the production of projectors, where p is the wholesale price (in dollars) of X P\") 06) a projector for an annual demand of x projectors and C is the total cost (in dollars) of producing x projectors. Answer the following questions 390 556 119,000 (A) - (D) 410 379 129,600 530 196 168,000 870 94 192,000 (A) Find a quadratic regression equation for the price-demand data, using x as the independent variable. y = (Type an expression using x as the variable. Use integers or decimals for any numbers in the expression. Round the coefcients to seven decimal places as needed. Round the constant term to three decimal places as needed.) The table to the right contains price-demand and total cost data for X p($) C($) the production of projectors, where p is the wholesale price (in 410 610 110,000 dollars) of a projector for an annual demand of x projectors and C 530 374 135, 100 is the total cost (in dollars) of producing x projectors. Answer the 690 223 172,000 following questions (A) - (D). 930 70 149,000 . . . (A) Find a quadratic regression equation for the price-demand data, using x as the independent variable. First input the values in the x and p columns of the table into a table on your graphing calculator. Then perform a quadratic regression on these values having the x-values being the independent variables and the p-values being the dependent variables. Find the quadratic curve of best fit for the price-demand data. Reference your calculator manual to determine how to perform a quadratic regression using points in a table. y = 0.0016504x - 3.2217826x + 1642.649 (B) Find a linear regression equation for the cost data, using x as the independent variable. Use this equation to estimate the fixed costs and variable costs per projector. Input the C-values into a third column in the table on your calculator. Then run a linear regression on points with the x-values being the independent variables and the C-values being the dependent variable. Calculate the line of best fit for the cost data. Reference your calculator manual to determine how to perform a linear regression using points in a table. y = 76.84x + 92,347.16 Now determine the fixed and variable costs per projector. Recall that the cost function is C = (fixed costs) + (variable costs).\"w Fixed costs are costs that include things like plant overhead costs, product design, and setup. These costs are not a dependent on how many items are produced. Variable costs are costs that include things like materials, labor, and transportation. These costs are the part of the cost function that changes depending on how much product is produced. The xed costs is the constant term in the cost function. Thus, the xed costs are approximately $92,347. The variable costs is the coefcient of x in the cost function. Thus, the variable costs are approximately $77 per projector. (0) Find the break even points. Recall that break-even points are the points where the revenue and cost functions intersect. They are called break-even points because revenue equals cost at these production levels. The break-even points must be in the domain of the price-demand equation. Graph the price-demand equation to nd the correct domain. Price, p, and demand, x, must both be nonnegative. The domain should also only include the part of the graph of the equation that has a negative slope since when price increases, the demand should decrease. Determine the domain of the price-demand function p = 0.0016504x2 - 3.2217826x + 1642.649. 0 s x s 976 (Rounded) Remember that the revenue function, R, is the number of items sold, x, multiplied by the price per item, p. The Remember that the revenue function, R, is the number of items sold, x, multiplied by the price per item, p. The revenue function will have the same domain as the price-demand equation. The revenue function is calculated below. R = xp = x (0.0016504x2 3.2217826x + 1542.649) = 0001050403 3.2217026x2 + 1642.649): Graph the revenue and cost function in the same window. Q a V. a 0 S x s 1000 0 s y 5 300,000 There appear to be two break-even points that are in the domain of the price-demand equation. Use the intersect tool on your graphing calculator to nd each break-even point. Find the leftmost break even point. Round each R = XP =x (0.0016504x - 3.2217826x + 1642.649) = 0.0016504x3 - 3.2217826x2+ 1642.649x Graph the revenue and cost function in the same window. + OSXS 1000 0 sys 300,000 There appear to be two break-even points that are in the domain of the price-demand equation. Use the intersect tool on your graphing calculator to find each break-even point. Find the leftmost break even point. Round each coordinate the the nearest integer. (68,97589)Now find the break-even point on the right. Round each coordinate the the nearest integer. (683, 144830) Notice that both ordered pairs are in the domain of the price demand equation. Thus, the break even points are (68,97589) and (683, 144830). (D) Find the price range for which the company will make a profit. Remember that a company makes a profit when revenue is + greater than cost. Notice in the graph of the revenue and cost functions that the revenue is greater than the cost between the two break even points. Find the price range for which the company will make a profit by substituting the x-coordinate of each break-even ordered pair into the price-demand equation. Substitute x = 68 into the price-demand equation and simplify. p = 0.0016504x2- 3.2217826x + 1642.649 = 0.0016504(68)- - 3.2217826(68) + 1642.649