

1. 
The profit for each unit of lumber is $40 and the profit for each unit of plywood is $60. Write a profit function P(x, y) if x = the number of units of lumber and y = the number of units of plywood. 


A. 
P(x, y) = 60x  40y 
B. 
P(x, y) = 40x  60y 


C. 
P(x, y) = 60x + 40y 
D. 
P(x, y) = 40x + 60y 


Hint 


2. 
Use the function P(x, y) = 40x + 60y to determine how many of each item should be produced in order to maximize profit. 


A. 
(100, 400) 
B. 
(300, 500) 


C. 
(500, 400) 
D. 
(100, 800) 


Hint 


3. 
Find the maximum value of f(x, y) = 2x + y  4 for the system of inequalities: y 3x + 1 y x  4 x 0 y 0 


A. 
alternate optimal solutions 
B. 
unbounded 


C. 
2 
D. 
infeasible 


Hint 


4. 
Sam has $10,000 to deposit in two different savings accounts. He wants at least $3,000 in the account that earns 3% interest. He wants no less than $5,000 in the account with 7% interest. Write a system of inequalities to represent this situation. 


A. 
x 3000 y 5000 x + y 10,000 
B. 
x 3000 y 5000 x + y 10,000 


C. 
x 5000 y 3000 x + y 10,000 
D. 
x 3000 y 5000 x + y 10,000 


Hint 


5. 
Sam has $10,000 to deposit in two different savings accounts. He wants at least $3,000 in the account with 3% interest. He wants no less than $5,000 in the account with 7% interest. For the equation l(x, y) = 30x + 70y find the maximum interest if the vertices are (3,5), (3,7) and (5,5) 


A. 
580 
B. 
500 


C. 
440 
D. 
no maximum 


Hint 

