# A tailor makes two types of garments A and B. Garment A requires 3 metres of material while garment B requires 2 ½ metres of material. The tailor uses not more than 600 metres of material daily in making both garments. He must make not more than 100 garments of type A and not less than 80 of type B each day.

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A tailor makes two types of garments A and B. Garment A requires 3 metres of material while garment B requires 2 ½ metres of material. The tailor uses not more than 600 metres of material daily in making both garments. He must make not more than 100 garments of type A and not less than 80 of type B each day.

1. Write down all the inequalities from this information.
2. Graph the inequalities above
3. If the business makes a profit of shs. 80 on garment A and a profit of shs. 60 on garment B, how many garments of each type must it make in order to maximize the total profit?

1. Write down all the inequalities from this information.
(i) 3x + 2 1/2y ≤ 600
(ii) x ≤ 100
(iii) Y ≥ 80, x ≥ 0

2. Graph the inequalities above

line 3x + 2 1/2y ≤ 600
Line x ≤ 100
Line ≥ 80, x ≥ 0

3. If the business makes a profit of shs. 80 on garment A and a profit of shs. 60 on garment B, how many garments of each type must it make in order to maximize the total profit?
The objective functions
P = 80x + 60y
100 garments of type A
120 garments of type B