A freight company has shipping orders for two products. The first product has a unit volume of 10 cu ft and weighs 50 lb. The second product's unit volume is 3 cu ft, and it weighs 40 lb. If the company's trucks have 2,450 cu ft of space and can carry 22,000 lb, how many units of each product can be transported in a single shipment with one truck using the entire volume and weight capacity?

A hollow metal sphere has a wall thickness of 2cm. If you increase both the diameter and thickness of this sphere so that the overall volume is three times the original overall volume, how thick will the shell of the new sphere be?

A solar power field is located on the south bank of a straight river that is 2 km wide. A power line is to be constructed from the solar field to an electric substation located on the north bank of the river 4 km east of the solar field. The cost of running the power line is $100,000/km overland and $200,000/km under the river. To minimize the cost of the power line, how much of the power line should be run overland?

An excavation company has been contracted to supply 10 million cubic feet (cu. ft.) of dirtto a construction site. The company uses a bulldozer to collect dirt, which is then moved by adump truck to the construction site. It costs the company $100 per hour to use the bulldozer,and it rents dump trucks at a rate of $40 per hour per truck. Each dump truck can hold 1,000cu. ft. of dirt, and it takes an average of 12 minutes for the bulldozer to load a dump truckwith dirt. It takes an average of five minutes for a fully loaded dump truck to deliver the dirtto the construction site and returns to the bulldozer for another load.Assume that the time to load a dump truck and the time for a dump truck to deliver the dirtto the construction site and return to the bulldozer follow exponential distributions. Moreover,a usual trip of the truck involves load with dirt, deliver the dirt, return to the bulldozer whereit joins a queue for another load of dirt.Then, determine the most appropriate…