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Formulate inequalities for the given constraints on the number of dresses (x) and suits (y) and represent them graphically.

Mathematics

ScanSolve AI Answer

Answer

a(iii)

2x+3y≥1502x + 3y \ge 150

Step-by-step solution

2 steps

Here's the solution to the problem:

Part a(i)

The number of dresses should not exceed 50.

Let xx be the number of dresses and yy be the number of suits.

x≤50x \le 50

Part a(ii)

The number of dresses should not be less than the number of suits.

x≥yx \ge y

Part a(iii)

2x+3y≥1502x + 3y \ge 150

The cost of making a dress is K140.00 and that of a suit is K210.00. The total cost should be at least K10 500.00.

140x+210y≥10500140x + 210y \ge 10500

Dividing by 10:

14x+21y≥105014x + 21y \ge 1050

Dividing by 7:

2x+3y≥150\boxed{2x + 3y \ge 150}

Additionally, since the number of dresses and suits cannot be negative:

x≥0x \ge 0 y≥0y \ge 0

Part b· 2 steps

To draw the graph and shade the unwanted region, follow these steps

  1. Draw the xx and yy axes on graph paper.

    Use a scale of 2cm to represent 10 units on both axes.
    Label the xx-axis from 0 to 60 and the yy-axis from 0 to 80.

  2. Draw the boundary lines for each inequality.

    • For x≤50x \le 50, draw the vertical line x=50x = 50.
    • For x≥yx \ge y (or y≤xy \le x), draw the line y=xy = x. (Points: (0,0),(10,10),(50,50)(0,0), (10,10), (50,50))
    • For 2x+3y≥1502x + 3y \ge 150, draw the line $2x + 3y = 150
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