Urgently help on this D1 question

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l33t h4x0r
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this question appeared on past D1 paper which i cannot find a solution...so if any of u got a solution for D1 paper please post it up!!! Im kind stuck with this question right now, please HELP!!!
here's the question:
A manager wishes to purchase seats for a new cinema. He wishes to buy three types of seat; standard, deluxe and majestic. Let the number of standard, deluxe and majestic seats to be bought be x, y and z respectively.
He decides that the total number of deluxe and majestic seats should be at most half of the number of standard seats.
The number of deluxe seats should be at least 10% and at most 20% of the total number of seats.
The number of majestic seats should be at least half of the number of deluxe seats.
The total number of seats should be at least 250.
Standard, deluxe and majestic seats each cost £20, £26 and £36, respectively.
The manager wishes to minimize the total cost, £C, of the seats.
Formulate this situation as a linear programming problem, simplifying your inequalities so that all the coefficients are integers.
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Originally posted by l33t h4x0r
this question appeared on past D1 paper which i cannot find a solution...so if any of u got a solution for D1 paper please post it up!!! Im kind stuck with this question right now, please HELP!!!
here's the question:
A manager wishes to purchase seats for a new cinema. He wishes to buy three types of seat; standard, deluxe and majestic. Let the number of standard, deluxe and majestic seats to be bought be x, y and z respectively.
He decides that the total number of deluxe and majestic seats should be at most half of the number of standard seats.
The number of deluxe seats should be at least 10% and at most 20% of the total number of seats.
The number of majestic seats should be at least half of the number of deluxe seats.
The total number of seats should be at least 250.
Standard, deluxe and majestic seats each cost £20, £26 and £36, respectively.
The manager wishes to minimize the total cost, £C, of the seats.
Formulate this situation as a linear programming problem,
simplifying your inequalities so that all the coefficients are integers.
y + z <= 1/2x ===> 2(y+z) <= x
y>=10/100(x+y+z) ===> x + z <= 9y
y>=20/100(x+y+z) ===> x + z >= 4y
z>=1/2y ====> 2z >= y

x+y+z>=250

function is to minimise cost = 20x + 26y + 36z


its pretty late but i think thats right
good luck tomorrow
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