Math

I need help in seeing if I solved these inequality problems correctly.

1. A store sells two models of computers. Because of the demand, the store stocks at least twice as many units of model A as of model B. The costs to the store for the two models are $800 and $1200, respectively. The management does not want more than $20000 in computer inventory at any one time, and it wants at least four model A and two model B computers in inventory at all times. Find and graph a system of inequalities describing all possible inventory levels.

I came up with this:

x = units of model A
y = units of model B

y <= 2x
800x + 1200y <= 20,000
x >= 4
y >= 2

2. For a concert event, there are $30 reserved seat tickets and $20 general admission tickets. There are 2000 reserved seats available, and fire regulations limit the number of paid ticket holders to 3000. the promoter must take in at $75000 in ticket sales. Find and graph a system of inequalities describing the different numbers of tickets that can be sold.

I came up with this:

x = number of reserved tickets
y = numbers of general tickets

30x <= 2000
20y <= 3000
30x + 20y <= 75000

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  1. 1--2(800A + 1200B = 20,000
    2--1600A + 1200B = 20,000
    3--4A + 3B = 50
    4--Dividing through by the smallest coefficient yields A+ A/3+B = 16+2/3
    5--(A - 2)/3 must be an integer k making A = 3k + 2
    6--Substituting back into (3) yields B = 14 - 4k
    7--k....0....2....3....4....5
    ...A....2....5....8...11...14
    ...B...14...10....6...2....-2

    Therefore, there are 4 possible inventory quantities.

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