Linear programming questions | form four Basic Mathematics

A girl wishes to buy skirts for herself. A white skirt costs 2,400/= per piece, while a coloured one costs
3,000/=. She intends to buy at most four white skirts. If she is prepared to spend up to 48,000/= in her  shopping, find the largest number of skirts she can buy.

Tea leaves are packed in packets of 20g, 50g and 90g. Find the smallest amount of tea leaves needed to give a whole number of packets of each size.

A bread dealer can buy up to 150 loaves of bread. Premium bread costs 200/= per loaf and Royal bread costs 250/= per loaf. The dealer can spend not more than 36,000/=  in the business. Premium bread sells at a profit of 40/= per loaf while, Royal bread sells at a profit of 50% per loaf. How many loaves of bread of each type should the dealer buy in order to generate a maximum profit?.

By shading the unrequired part, show the region represented by the following set of inequalities:



and

A manufacturer has 150 and 90 kilograms of wood and plastic respectively. Product A requires 1 kg
of wood and 2 kg of plastic. Product B requires 3 kg of wood and 1 kg of plastic. If A is sold for
Tsh. 4000/= and B for Tsh. 6000/=, how many of each should be made to obtain the maximum gross
income?

If B1 = { (x, y):x + y < 6, x, y R} and B2 = { (x, y): x- y < 2, x, y R}
draw the graphs ofB1 and B2 and shade the area represented by B1 B2•

Write down three inequalities which deflne the shaded area labelled A in the diagram below.

1. Draw using the same set of axes the following inequalities:

2x+y16

x+2y11

x+3y15

x0

y0

2. From the graph in (a) find the points which will make the function f(x, y) = 3x + 5y either a maximum or minimum.

Two tailors A and B spend shs. 15,000/= and shs. 20,000/= per day to make a shirt and a gown respectively. A can stitch 6 shirts and 4 gowns per day while B can stitch 10 shirts and 4 gowns per day. How many days shall each work if it is desired to stitch at least 60 shirts and 32 gowns at a minimum cost?

Two types of food, A and B, contain 4 and 6 units of protein, and 5 and 3 units of starch per kg respectively. The cost of A is shs. 400.00 per kg. The cost of  B is shs. 500.00 per kg. If the minimum daily intake is 16 units of protein and 11 units of starch, how much food should be bought in order to meet these conditions?