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?

Answer / Solution

UNSOLVED

Solve by graphical method the following system of simultaneous equations:

4x+y=6

5x+2y=9

Answer / Solution

UNSOLVED

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?

Answer / Solution

UNSOLVED

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.

Answer / Solution

UNSOLVED

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?.

Answer / Solution

UNSOLVED