Our quiz on Friday will be an application of the inequality solving techniques we/ve been using the last couple of days.

Harold has decided to order vases and statues from Larry to sell in his shop at the shore this summer.  Vases cost $200 each while the statues cost $500 each and he has $10000 to spend on inventory.   He also has $800 for shipping, handling and insurance where the cost per vase is $32 and the cost per statue is $20.  Suppose that he also must buy at least 10 vases and 5 statues.

Identify the variables and illustrate the set of solutions with a graph in the xy plane.

Let x = #vases and y = # statues. Then from the inventory budget we have

20x + 50 y  1000

and from the shipping and handling budget we have

32x + 20 y  800

we also have from the minimum purchase requirements that

x  10 and y  5.

Graph the bounding lines and shade the appropriate sides to determine the region of  the solution set.

--CFW