Answer the following
1. Solve the inequalities below:
2. Write down the inequality which describes the shaded region.
1. Solve the inequalities below:
2. Write down the inequality which describes the shaded region.
3. For shaded region, write down the 3 inequalities which describe it
4. A farmer has 80 hectares of his farm available for planting maize and cabbages. He must grow at least 10 hectares of maize and 20 hectares of cabbages to meet demands. He prefers to plant more cabbages than maize but his work force and equipment will only allow him to cultivate a maximum of three times the quantity of cabbages to that of maize.
(i)Represent the information above as a system of inequalities.
(ii)Sketch a graph of these inequalities.
(iii)If the profit on maize is R800 per ha and on cabbages R500 per ha, how should the farmer plant the two crops to make a maximum profit and what is this profit.
5. Sketch the following constraints by clearly indicating all intercepts with the axes and the feasible region :
2 ≤ x ≤6 ; y ≥ 1 ; 3x + 2y ≥ 12 ; 9y + 7x ≤ 63
Use the objective function P = 3x + 2y to maximize P with respect to the feasible region.
6. A factory makes two types of beds, type A and type B. Each month x of type A and y of type B are produced.
The following constraints control monthly production:
(i) Not more than 50 beds of type A and 40 beds of type B can be made.
(ii) To show a profit at least 60 beds in all must be made.
(iii) The maximum number of beds that can be produced is 80.
(iv) Write down in terms of x and y the inequalities that represent these constraints. Sketch a graph of these inequalities.
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