At a particular store, candy bars are normally priced at $1.00 each. last week, the store offered a promotion under which customers purchasing one candy bar at full price could purchase a second candy bar for $0.50. a third candy bar would cost $1.00, a fourth would cost $0.50, and so on. if, in a single transaction during the promotion, rajiv spent d dollars on n candy bars, where d and n are integers, is n even?

Abakery wants to determine how many trays of doughnuts it should prepare each day. demand is normal with a mean of 5 trays and standard deviation of 1 tray. if the owner wants a service level of at least 95%, how many trays should he prepare (rounded to the nearest whole tray)? assume doughnuts have no salvage value after the day is complete.

Suppose a firm faces a fixed price of output, 푝푝= 1200. the firm hires workers from a union at a daily wage, 푤푤, to produce output according to the production function 푞푞= 2퐸퐸12. there are 225 workers in the union. any union worker who does not work for this firm is guaranteed to find nonunion employment at a wage of $96 per day. a. what is the firm’s labor demand function? b. if the firm is allowed to choose 푤푤, but then the union decides how many workers to provide (up to 225) at that wage, what wage will the firm set? how many workers will the union provide? what is the firm’s output and profit? what is the total income of the 225 union workers? c. now suppose that the union sets the wage, but the firm decides how many workers to hire at that wage (up to 225). what wage will the union set to maximize the total income of all 225 workers? how many workers will the firm hire? what is the firm’s output and profit? what is the total income of the 225 union workers? [hint: to maximize total income of union, take the first order condition with respect to w and set equal to 0.]

Acompany 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 $3 on each unit of product a and $4 on each unit of product b. to manufacture a unit of product a requires 7 min on machine i and 5 min on machine ii. to manufacture a unit of product b requires 8 min on mchine i and 5 min on machine ii. there are 175 min available on machine i and 125 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?