Abakery sells rolls in units of a dozen. the demand x (in 1000 units) for rolls has a gamma distribution with parameters α = 3, θ = 0.5, where θ is in units of days per 1000 units of rolls. it costs $ 2 to make a unit that sells for $ 5 on the first day when the rolls are fresh. any leftover units are sold on the second day for $ 1. how many units should be made to maximize the expected value of the profit?

Pete is making decorations for a dinner party. the instructions tell him to use 9 flowers for a medium-sized decoration. complete each statement to adjust the flowers for different-sized decorations based on these instructions.

Acaterer knows he will need 60, 50, 80, 40 and 50 dinner napkins on five successive evenings. he can purchase new napkins initially at 25 cents each, after which he can have dirty napkins laundered by a fast one-day laundry service (i.e., dirty napkins given at the end of the day will be ready for use the following day) at 15 cents each, or by a slow two-day service at 8 cents each or both. the caterer wants to know how many napkins he should purchase initially and how many dirty napkins should be laundered by fast and slow service on each of the days in order to minimize his total costs. formulate the caterer’s problem as a linear program as follows (you must state any assumptions you make): a. define all variables clearly. how many are there? b. write out the constraints that must be satisfied, briefly explaining each. (do not simplify.) write out the objective function to be minimized. (do not simplify.)

What type of symmetry does a rhombus have?