Suppose a furniture builder has two models of a bookcase: standard and artisan. The standard model requires 5 hours to assemble and 1 hours for finishing touches. The artisan model requires 2 hours to assemble and 4 hours for finishing touches. Based on their current staffing, they can manage a maximum number of assembly hours available is 50 per day, and the maximum number of finishing hours available is 64 per day. Let x = the number of standard model bookcases produced per day and y = the number of artisan model bookcases produced per day. Write the system of inequalities that represents the maximum number of bookcases that can be produced in one day.

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The firm WebsAreUs creates and maintains Web sites for client companies. There are two types of Web sites: “Hot” sites change their layout frequently but keep their content for long times; “cool” sites keep their layout for a while but frequently change their content. Maintaining a hot site requires 1.5 hours of layout time and 2 hour for content changes. Maintaining a cool site requires 1 hour of layout time and 2 hr for content changes. Everyday WebsAreUs has 12 hrs available for layout changes and 16 hr for content changes on a hot site. Net profit is $50 for a set of changes on a hot site and $250 for a set of changes on a cool site. To maximize profit, how many of each type of site should WebsAreUs maintain daily? How, if at all, do the maximum profit and optimal policy change if the company must maintain at least two hot and 3 cool sites daily?

A tortoise and hare are competing in a 400-meter race. The arrogant hare gives the tortoise a 220-meter head start. When the start gun is fired, the hare begins running at a constant speed of 3.5 meters per second and the tortoise begins crawling at constant speed of 1.5 meters per second. Take out a piece of paper and read the above problem context again. You will prepare your written work and solutions on your own paper and upload it and the end of this question. Complete the problem solving process by: i. reading and re-reading the problem to identify the quantities in the situation; ii. making a drawing to represent the relevant quantities in the situation; iii. and defining the variable t to represent the number of seconds since the start of the race. a. Define a function f to determine the distance of the tortoise from the finish line in terms of the number of seconds, t, since the start of the race. Preview Solve f(t) = 0 and describe what your solution represents. t = Preview…