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Problem # 1 The feasible region shown below is bounded by lines Find the coordinates of corner points. Show your work.
Problem # 3
Perform the following operations:
4 -3 10
3 -2 1
(-2)R1 +R2 ->R2
4 -3 10
3 -2 1
2R1 +3R2 ->R1
Problem # 4 (you do not have to find x and y values)
There are 2 types of boxes: box A and box B.
Box A contains 2kg of apples and 4 kg of oranges, and sells for $ 10.
Box B contains 3kg of apples and 5 kg of oranges, and sells for $12. 5
10 kg of apples and 600 kg of oranges are available.
The company will try to sell the amount of each mixture (box A and box B) that maximize income.
Let x is the number of boxes A Let y is the number of boxes B
a) State the inequality that must be satisfied for apples:
b) State the inequality that must be satisfied for apples
c) State the objective function:
Problem # 5
A concert promoter wants to book a rock group for a stadium concert. A ticket for admission to the stadium playing field will cost $25, and a ticket for a seat in the stands will cost $35. The group wants to be guaranteed total ticket sales of at least $14,000. How many tickets of each type must be sold to satisfy the group's guarantee? Express the answer as a linear inequality and draw its graph.
Problem # 6
A store sells two types of albums, Red and Blue. The store owner pays $8 for a Red album and $14 for a Blue album. One Red album yields a profit of $2 while Blue album yields a profit of $3. The store owner estimates that no more than 2000 albums will be sold every month and he does not plan to invest more than $20,000 in inventory of these albums. How many units of each type of albums should be stocked in order to maximize his monthly total profit?
