- Problem B Your Company Has Received An Order From San Ramon S Recreation Department To Manufacture 6 000 Custom Kickboar 1 (99.17 KiB) Viewed 20 times
PROBLEM B Your company has received an order from San Ramon's recreation department to manufacture 6,000 custom kickboards for its summer swimming program. Your facility owns 20 machines, each of which can produce 30 kickboards an hour. It costs $20 to set up a machine to produce the kickboards. Once the machines have been set up, the operation is fully automated and can be overseen by a single production supervisor earning $25 per hour. a. Create the cost function for this contract. b. Use calculus to find the relative minimum for your cost function. c. How many of the machines should be used to minimize the cost of production? d. How much will the supervisor earn during the production run if the optimal number of machines is used? e. How much will it cost to set up the optimal number of machines? Problem C A power line is to be run from a power plant on one side of a 1-kilometer wide river to a business on the other side of the river located 4 kilometers downstream. The run is to consist of two parts: the first part is to go straight down the shoreline, costing $50 per meter, while the second part is to go underwater and straight toward the business, costing $100 per meter. FIND THE DISTANCES FOR LAND AND WATER THAT MINIMIZE THE COST. Powerline on land x km 1 km Powerline Under Water √1+(4-x)² km 4 km SHOP com PROBLEM D The manager of a department store decides to build a 600-square foot rectangular enclosure on the store's parking lot in order to display some equipment. Three sides of the enclosure will be built of redwood fencing, at a cost of $14 per running foot. The fourth side will be built of cement blocks, at a cost of $28 per running foot. cement blocks ******* 1. Find the dimensions of the enclosure that will minimize the total cost of the building materials. 2. is the minimum materials cost? Several customers notice the manager's craftmanship. She decides to set-up a side hustle and takes orders to build enclosures for customers' homes. She experiments with pricing and notices that she can sell 6 enclosures when priced at $2000 each. For every $500 increase in price, she sells one less enclosure. 3. How many enclosures should she produce a month to maximize her profit? Note: since she is building the enclosures herself, she doesn't have any labor costs. Use your materials cost from Part 2 to set-up your cost function.