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Solve the linear programming problem by sketching the region and labeling the vertices, deciding whether a solution exists, and then finding it if it does exist. (If an answer does not exist, enter DNE.)

Minimize	C = 5x + 20y
Subject to	2x + 5y ≥ 20 x ≥ 0,  y ≥ 0

C = 1

Formulate the situation as a system of inequalities. (Let x represent the number of dinghies the company can manufacture and y represent the number of rowboats.)

A boat company manufactures aluminum dinghies and rowboats. The hours of metal work and painting needed for each are shown in the table, together with the hours of skilled labor available for each task. How many of each kind of boat can the company manufacture?

(hours)	Dinghy	Rowboat	Labor Available
Metal Work	2	3	108
Painting	2	2	90
1 (labor for metal work) 2 (labor for painting)  x ≥ 0, y ≥ 0

Find the vertices. (Order your answers from smallest to largest x, then from smallest to largest y.)

Please sketch the graph. (x, y) =  4

(x, y) =  5

(x, y) =  6

(x, y) =  7

Solve the system by graphing. (Enter your answers as a comma-separated list. If the system is inconsistent, enter INCONSISTENT. If the system is dependent, enter DEPENDENT.)

x + y = 10
x − y = 6
(x, y)	=		1

You have just won $110,000 from a lottery. If you invest all this amount in a tax-free money market fund earning 6% compounded weekly, how long do you have to wait to become a millionaire? (Round your answer to two decimal places.) 1 yr

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