A rectangular piece of cardboard measuring 12 in by 18 in is to be made into a box by cutting equal size squares from each corner and folding up the sides. Let x represent the length of a side of each such square in inches. Complete parts (a) through (d) below. (a) Give the restrictions on x. (b) Determine a function V that gives the volume of the box as a function of x. (Round to the nearest hundredth.) (c) For what value of x will the volume be a maximum? (Round to the nearest hundredth.) (d)The volume will be greater than 80 cubic inches when (Type an integer or a decimal. Round to the nearest thousandth.)

Carla was trying to decide what to do saturday evening. she has $100 available to spend for the evening. she has narrowed her choices down to these events: braves game, a concert of an artist she likes, or the georgia aquarium. admission to the braves game is $25, hot dogs cost $10, sodas cost $5. the concert costs $25 for admission, $20 for a souvernir t-shirt, and $10 for a soda. the georgia aquarium has the show of a lifetime with an all you can eat and drink that costs $100. carla does not want to take any driving chances, so in addition to the cost of the aquarium, she will also need to pay for her uber/lyft, which is $15 each way. which option should carla choose if she wants to spend the least? based on that choice, what then is carla's oppotunity cost? fully explain your answer in at least one paragraph.