3. Show that the area of the optimal rectangle inscribed inside a semi- circle of radius 2 (found in the video "Optimization Examples") is indeed a maximum, using either the first or second derivative rule.
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- Find the maximum and minimum value. Based on the result, is 1 girl in 10 births a significantly low number of girls?A company handles an apartment building with 50 units. Experience has shownthat if the rent for each of the units is $720 per month, all of the units will be lled, but 1unit will become vacant for each $20 increase in this monthly rate. At what price is revenuemaximum? What is the maximum revenue and how many apartments are rented to reachthis max?1Suppose that the Best Custom Calendar Company models the coming year's revenuse and cost functions, in thousands of dollars, to be R(x)= -x^3+9x^2 and C(x)=2x^3-12x^2+30x, where x represents units of 1000 calendars and where teh model is thought to be accurate up to approximately x=5.5. Round the dollar amounts to the nearest dollar. What is the profitable zone of calendar production levels? What is the maximum profit and the level of production that will generate the maximum profit? What is the maximum loss and the level of production generating this maximum loss when the ompnay is not in the profitable zone?
- Provide a detailed solution and conclusion (without the use of piecewise function): The rate at which the total average number of COVID cases is increasing at x=10 tents and dxdt=1 tent per day, Given that if 25 tents are built, the average number of COVID cases per tent will be 6 cases while the average number of cases will increase by 2 per tent for each additional tent in the same area due to overcrowding.A manufacturing company had won a contract to supply 109200 units of a product to a customer.The production planing and control department of the company has estimated the production in the first week to be 8,000 units,but that by recruiting and training some extra staff,output will rise by 200 units each week . a. When would the company be able to complete the contract. B.If the recruitment of staff does not go as well as expected so that after six weeks ,weekly production remains constant at the level achieved in the sixth week.how long would it take to complete the contract