Linear programming questions | form four Basic Mathematics

Ally wishes to buy up to 40 notebooks for his stationery. He can buy either type A for sh.3,000 each or type B for sh.6,000 each. He has a total of sh. 150,000 to spend and he have at least 10 notebooks of type A and at least 5 notebooks of type B in his stock.

1. Write down all the inequalities which represent the given information.
2. If he makes a profit of sh. 400 on each notebook of type A and sh. 1,000 on each notebook of type B, how many notebooks of each type he should buy for maximum profit?

Solve by graphical method the following system of simultaneous equations:

4x+y=6

5x+2y=9

A farm is to be planted with sorghum and maize while observing the following constraints:

If sorghum yields a profit of 800,000 shillings per hectare while maize yields 600,000 shillings per hectare, how many hectares should be planted with each crop for maximum profit?

Anna and Mary are tailors. They make x blouses and y skirts each week. Anna does all the cutting and Mary does all the sewing. To make a blouse it takes 5 hours of cutting and 4 hours of sewing. To make a skirt it takes 6 hours of cutting and 10 hours of sewing. Neither tailor works for more than 60 hours a week.

1. For sewing show that 2 x + 5 y ≤ 3 0
2. Write down another inequality in x and y for the cutting.
3. If they make at least 8 blouses each week, write down another inequality.
4. Using 1cm to represent 1 unit on each axis, show the information in parts (a), (b) and (c) graphically. Shade only the required region.
5. If the profit on a blouse is shs. 3,000/= and on a skirt is shs. 10,000/=, calculate the maximum profit that Anna and Mary can make in a week.

The number of units of proteins and starch contained in each of two types of food A and B are shown in the table below:

What is the cheapest way of satisfying the minimum daily requirement?.

Maximize f=2y-x subject to the following constraints:

x>=0

y>=0

2x+y<=6

x+2y<=6

Sara had 300 shillings to buy erasers and pencils. An eraser cost 20 shillings while a pencil costs 30 shillings. If the number of erasers bought is at least twice the number of pencils, formulate the inequalities that represent this information.