where p is measured in dollars and * is measured in units of a thousand. To yield a maximum revenue, how many watches must be sold? Find the production level that will maximize the revenue, the maximum revenue, and the price that the company needs to charge at that level 4. [20 Points] The weekly demand for wireless mice manufactured by Insignia Consumer Electronic Products group is given by p(x) = -.0005x + 60 where p denotes the unit price in dollars and a denotes the quantity demanded. The weekly cost function associated with producing these wireless mice is given by C(x) = -0.001x + 18x + 4000 Where C(x) denotes the total cost in dollars incurred in pressing x wireless mice. (=) Find the production level that will yield a maximum revenue for the manufacturer. What will be maximum revenue? What price the company needs to charge at that level? (b) Find the production level that will yield a maximum profit for the manufacturer. What will be maximum profit? What price the company needs to charge at that level? 5. [10 Points] A bee farmer estimates that the first 10,000 jars of honey produced this quarter will fetch a profit of $5/jar. But if more than 10,000 jars of honey were produced, the profit per jar for the entire lot would drop by $0.0002 for each additional jar produced and sold. Assuming that at least 10,000 jars of honey are produced and sold, what is the maximum profit? How many more jars must be produced and sold to get the maximum profit? [10 Points] The demand for a small sedan tires imported by Michelin Tires is 100,000/year and may be assumed to be uniform throughout the year. The cost of ordering a shipment of tires is $1000, and the cost of storing each tire for a year is $5. Determine how many tires should be in each shipment if the ordering and storage costs are to be minimized. (You may also assume that each shipment arrives just as the previous one has been sold.) 7. [10 Points] With more than 300 million USD invested since 2012, drone deliveries will become the fastest-growing application method within the drone market, according to DRONEII': 2019 Drone Delivery report. Drone regulations for the delivery of medical products between hospitals and laboratories specify that medical products sent by drones using a rectangular box may have a combined length (1) and girth (x + x + x + x = 4x ) of no more than 100 in (see the figure below). Find the dimensions of a rectangular box that has a square cross section and the largest volume that may be used by drones