A company manufactures x units of product A and y units of product B, on two machines, I and II. It has been determined that the company will realize a profit of $2 on each unit of product A and $5 on each unit of product B. To manufacture a unit of product A requires 5 min on machine I and 3 min on machine II. To manufacture a unit of product B requires 9 min on machine I and 4 min on machine II. There are 95 min available on machine I and 57 min available on machine II in each work shift. How many units of a product should be produced in each shift to maximize the company's profit P?

In new york city at the spring equinox there are 12 hours 8 minutes of daylight. the longest and shortest days of the year very by two hours and 53 minutes from the equinox in this year the equinox falls on march 21 in this task you use trigonometric function to model the hours of daylight hours on certain days of the year in new york city a. what is the independent and dependent variables? b. find the amplitude and the period of the function. c. create a trigonometric function that describes the hours of sunlight for each day of the year. d. graph the function you build in part c. e. use the function you build in part c to find out how many fewer daylight hours february 10 will have than march 21. you may look at the calendar.