QUESTION 4 4.1A company manufactures two types of games, Xbox and play station. Given below are the constrains faced by the company on a weekly basis. eet $$ x $$ represent Xbox and $$ y $$ represent play station. $$ 2 \leq x \leq 5 $$ $$ \leq y \leq 6 $$ $$ x+5 y \leq 40 $$ 1.1 Sketch the graph with the given constraints 1.2 Determine the feasible region 1.3 Determine how many of each can be sold every week so that the

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To solve this problem, we need to first sketch the graph with the given constraints and then determine the feasible region.

Given constraints:
1. $$ 2 \leq x \leq 5 $$
2. $$ 2 \leq y \leq 6 $$
3. $$ x + 5y \leq 40 $$

1.1 Sketch the graph with the given constraints:
To sketch the graph, we need to plot the lines representing the constraints on a coordinate plane.

1. Plot the lines $$ x = 2 $$ and $$ x = 5 $$ on the x-axis.
2. Plot the lines $$ y = 2 $$ and $$ y = 6 $$ on the y-axis.
3. Plot the line $$ x + 5y = 40 $$ on the coordinate plane.

1.2 Determine the feasible region:
The feasible region is the area where all the constraints are satisfied. In this case, the feasible region is the area below the line $$ x + 5y = 40 $$ and within the boundaries of the constraints.

1.3 Determine how many of each can be sold every week so that the total profit is maximized:
To maximize the total profit, we need to find the point in the feasible region that maximizes the profit function. However, the profit function is not provided in the problem. Therefore, we cannot determine the exact number of Xbox and PlayStation games that can be sold every week to maximize the total profit.

If you provide the profit function, I can help you determine the optimal number of games to sell.
To determine how many Xbox and PlayStation games can be sold each week, follow these steps: 1. **Graph the Constraints**: - Draw the lines $$ x = 2 $$, $$ x = 5 $$, $$ y = 2 $$, and $$ y = 6 $$ on a coordinate plane. - Plot the line $$ x + 5y = 40 $$. 2. **Identify the Feasible Region**: - The feasible region is the area where all constraints overlap, below $$ x + 5y = 40 $$, and within $$ 2 \leq x \leq 5 $$ and $$ 2 \leq y \leq 6 $$. 3. **Maximize Profit**: - Without the profit function, we cannot determine the exact number of each game to sell for maximum profit. - If the profit function is provided, use it to find the optimal point in the feasible region. **Conclusion**: With the given constraints, the feasible region is identified, but the exact number of Xbox and PlayStation games to sell for maximum profit cannot be determined without the profit function.

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