Santa Claus is assigning elves to work a shift making toy trucks. Apprentice elves draw a wage of 40 candy canes per shift, but can only make 32 trucks in a shift. Senior elves can make 48 trucks a shift and are paid 64 candy canes per shift. There is only room for 9 elves in the truck shop, and due to a candy-makers strike, Santa Claus can only pay out 480 candy canes for the whole 8-hour shift. What is the maximum number of trucks that can be built during the shift and how many of each type of elf should Santa assign in order to get that many trucks? Using the information in the problem, write the constraints. Let x represent the number of apprentice elf shifts, and y represent the number of senior elf shifts.
Total number of candy canes Santa has available to split between the elves: QUESTION
X+64 Y QUESTION 480 (QUESTION IS LESS THAN, GREATER THAN, LESS THAN OR EQUAL, OR GREATER THAN OR EQUAL)
Total number of elves that can that can be in the shop: QUESTION x + QUESTION y QUESTION (LESS THAN, GREATER THAN, LESS THAN OR EQUAL, GREATER THAN OR EQUAL) 9
How would you show that we cannot have a negative number of senior elves?: y QUESTION (LESS THAN, GREATER THAN, LESS THAN OR EQUAL, GREATER THAN OR EQUAL) QUESTION
Vertices of the feasible region: (0,0) (QUESTION, QUESTION) , (0, QUESTION) (QUESTION, 0)
Optimization equation: Number of trucks = 32 X + QUESTION y
Santa's maximum number of trucks is QUESTION. He should schedule QUESTION apprentice elves and QUESTION senior elves.