The paper screening for each idea takes 2 hours of a staff member’s time. after that, there is a stage of designing and producing a prototype. a designer spends 4 hour designing the game in a computer-aided-design (cad) package. the actual creation of the mock-up is outsourced to one of many suppliers with essentially limitless capacity. it takes 4 days to get the prototype programmed, and multiple prototypes can be created simultaneously. a staff member of the testing team needs 1 days to test an idea. running the focus group takes 2 hours of a staff member’s time per idea, and only one game is tested in each focus group. finally, the management team meets for 3 hours per idea to decide if the game should go into production. available working hours for each staff member are 8 hours per day, 5 days a week. the current staffing plan is as follows: a. paper screening: 3 staff members. b. design and production: 4 staff members. c. testing: 6 staff members. d. focus group: 1 staff member. e. finally decision: 1 management team. what is the implied utilization of testing team in percentage?

5. profit maximization and shutting down in the short run suppose that the market for polos is a competitive market. the following graph shows the daily cost curves of a firm operating in this market. 0 2 4 6 8 10 12 14 16 18 20 50 45 40 35 30 25 20 15 10 5 0 price (dollars per polo) quantity (thousands of polos) mc atc avc for each price in the following table, calculate the firm's optimal quantity of units to produce, and determine the profit or loss if it produces at that quantity, using the data from the previous graph to identify its total variable cost. assume that if the firm is indifferent between producing and shutting down, it will produce. (hint: you can select the purple points [diamond symbols] on the previous graph to see precise information on average variable cost.) price quantity total revenue fixed cost variable cost profit (dollars per polo) (polos) (dollars) (dollars) (dollars) (dollars) 12.50 135,000 27.50 135,000 45.00 135,000 if the firm shuts down, it must incur its fixed costs (fc) in the short run. in this case, the firm's fixed cost is $135,000 per day. in other words, if it shuts down, the firm would suffer losses of $135,000 per day until its fixed costs end (such as the expiration of a building lease). this firm's shutdown price—that is, the price below which it is optimal for the firm to shut down—is per polo.

Bakery has bought 250 pounds of muffin dough. they want to make waffles or muffins in half-dozen packs out of it. half a dozen of muffins requires 1 lb of dough and a pack of waffles uses 3/4 lb of dough. it take bakers 6 minutes to make a half-dozen of waffles and 3 minutes to make a half-dozen of muffins. their profit will be $1.50 on each pack of waffles and $2.00 on each pack of muffins. how many of each should they make to maximize profit, if they have just 20 hours to do everything?

What are the period and vertical shift of the cosecant function below? period: ; vertical shift: 1 unit up period: ; vertical shift: 2 units up period: ; vertical shift: 1 unit up period: ; vertical shift: 2 units up?