Question

A candy box is made from a piece of cardboard that measures 25 by 14 inches. Squares of equal size will be cut out of each corner. The sides will then be folded up to form a rectangular box. Find the length of the side of the square that must be cut out if the volume of the box is to be maximized. What is the maximum volume? 14 in. A square with a side of length of 2.88 inches should be cut away from each corner to maximize the volume. (Round to two decimal places as needed.) The maximum volume iscubic inches (Round to two decimal places as needed.) Question Help 12.3.27 A manufacturer of aluminum doors currently is able to sell 600 doors per week at a price of $85 each. If the price were lowered to $75 each, an additional 50 doors per week could be sold. Estimate the current elasticity of demand for the doors, and also estimate the current value of the manufacturers marginal-revenue function. The elasticity of demand for the doors is approximately Type an integer or a decimal. Do not round until the final answer. Then round to the nearest hundredth as needed.) Find the absolute maximum and minimum values of the function, if they exist, over the indicated interval. Also indicate the x-value at which each extremum occurs fx)7 271 2/3 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. 0 A. The absolute maximurm value is | and the absolute minimum value is | | at x at x- (Use a comma to separate answers as needed.) O B. The absolute maximum value is at x-and there is no absolute minimum. (Use a comma to separate answers as needed.) O C. The absolute minimum value isand there is no absolute maximum. (Use a comma to separate answers as needed.) O D. There is no absolute minimum and there is no absolute maximum. 3.6.8 Question Help For given a supply equation and demand equation for a product. If p represents price per unit in dollars and q represents the number of units per unit of time, find the equilibrium point. 2320 Supply equation is+10, demand equation is p g 20 The equilibrium point is (a.p) Type an ordered pair, using integers or fractions. Type an exact answer, using radicals as needed.)

Answer 1

-1 21 25 Volumxwxh (25-29(14-2%) (21) To gt maximum Volum 2.

By Quadratic for mula 2(6) + J 1834 12 724 43-405 12- lo Nenw 2. ot χ= 2,88 12 (2.8 -78 d"V 11(10-11)-18-43. 32 >O -

2.88 a Maximu mVolum at Maximum Volume = (25-2(2.88)][14-2(2.88)] (2, 88) (12v) (3 24) (2-3.) 9-2) (2 83) -456.59 i3