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Formulate inequalities for the number of chairs of type A (x) and type B (y) given the constraints on cost and minimum production numbers.

Mathematics

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Answer

x+y≤70\mathbf{x + y \le 70}

x≥20\mathbf{x \ge 20}

y≥10\mathbf{y \ge 10}

Step-by-step solution

4 steps

7. (a)

  1. Define the variables based on the problem statement.

    Let xx be the number of chairs of type A.
    Let yy be the number of chairs of type B.

  2. Formulate the inequality for the total cost.

    The cost of making one chair of each type is K2 000.00.
    The total cost for xx chairs of type A and yy chairs of type B is 2000x+2000y2000x + 2000y.
    The shop has K140 000.00 available, meaning the total cost cannot exceed this amount.

    2000x+2000y≤1400002000x + 2000y \le 140000

    Divide the entire inequality by 2000 to simplify:

    2000x2000+2000y2000≤1400002000\frac{2000x}{2000} + \frac{2000y}{2000} \le \frac{140000}{2000} x+y≤70x + y \le 70

  3. Formulate the inequality for the number of chairs of type A.

    The number of chairs of type A must be at least 20. "At least" means greater than or equal to.

    x≥20x \ge 20

  4. Formulate the inequality for the number of chairs of type B.

    The number of chairs of type B must be at least 10. "At least" means greater than or equal to.

    y≥10y \ge 10

    The three inequalities are:

    x+y≤70\boxed{\mathbf{x + y \le 70}} x≥20\boxed{\mathbf{x \ge 20}} y≥10\boxed{\mathbf{y \ge 10}}
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