Question

1. When a commercial bakery employs w full time bakers, the daily costs, in dollars, is given by C(w)= 400w+ 1200√w, where C(w ) is in dollars. In order to produce x loaves of bread each day, they need w(x)= 0.005x+750/x bakers. The bakery currently supplies 500 loaves of bread each day. At what rate is the daily costs changing with respect to the number of loaves of bread they supply? Include units!

2.The number of babies born in a certain city is modeled by ?(?)=800+115?+0.2?^2 , where ?? is the number of years since 2010. At what rate is the number of babies born changing with respect to time, in 2019? Round your answer to the nearest whole.

3.When a factory that produces wheelchairs spends ? dollars, they can produce ?(?)=400?^1/3wheelchairs a week. The amount of money they can spend is given by ?(?)=4?^2+70?+325 dollars, where ? represents the number of weeks since production began. At what rate is the number of wheelchairs the factory produces changing with respect to time, 20 weeks into production? Note: Part of the answers involves messy decimals. Keep at least 8 decimals in your calculation and round your final answer to 2 decimal places.

4.Paramount Electronics has an annual profit and is given by ?(?)=−100,000+5,000? −0.25?^2 in dollars, where ? is the number of laptops it sells each year. The number of laptops the company makes depends on the number of electrical engineers it employs, ?, and is given by ?(?)=30?+0.01?^2

Paramount Electronics currently employees 53 electrical engineers. Find the rate at which its profit is changing with respect to the number of electrical engineers it employees.

5. A company produces grain and the amount of grain it produces is measured by weight, in pounds. The weight of the grain, in pounds, is given by ?(?)=4000?^1/3, where ? represents the hours of labor used. The hours of labor depend on the time of year and is given by ?(?)=100+20√?−?, where ? is measured in months. At what rate will grain production be changing with respect to time 9 months from now?

6. A consultant determines that the annual profit of a certain company, (in dollars) is given by the equation ?(?)=−200,000+4,000? −0.4?^2−0.00001?^3, where ? is the number of surgical lasers it sells each year. The consultant also informs the company that the number of surgical lasers it can manufacture each year depends on the number of workers it employs and is given by the equation ?(?)=100?. At what rate if the profit changing with respect to the number of works when the company employees 20 workers?

please help with all these questions

Answer 1