Currently, you sell 40,000 units of a product for $45 each. the unit variable cost of producing the product is $5. you are thinking of cutting the product price by 30 percent. you are sure this will increase sales by an amount from 10 percent to 50 percent. perform a sensitivity analysis to show how profit will change as a function of the percentage increase in sales. ignore fixed costs. (hint: for cell d10; new profit is $1,378,000 with a 30% price cut percentage and a 30% sales increase.)

David paid $975,000 for two beachfront lots in coastal south carolina, with the intention of building residential homes on each. two years later, the south carolina legislature passed the beachfront management act, barring any further development of the coast, including david's lots. when david files a complaint to seek compensation for his property, south carolina refuses, pointing to a passage in david's own complaint that states "the beachfront management act [was] properly and validly designed to south carolina's " is south carolina required to compensate david under the takings clause?