graph the following : Let's denote the number of refrigerators to be produced as 'x' and the number of stoves as 'y'. The profit function to be maximized is P = 60x + 50y. arrow_forward Step 3 The constraints for the problem are as follows: - Assembly time: 4x + 10y <= 100 - Inspection time: 2x + y <= 22 - Storage space: 3x + 3y <= 39 arrow_forward Step 4 We can simplify the storage space constraint to x + y <= 13 since both products require the same amount of storage space. arrow_forward Step 5 The feasible solution space is the set of values (x, y) that satisfy all the constraints. This is a region bounded by the lines x + y = 13, 4x + 10y = 100, and 2x + y = 22. arrow_forward Step 6 To find the point that maximizes the profit, we need to evaluate the profit function at the corners of the feasible region. These corners are the points where the constraint lines intersect. arrow_forward Step 7 By solving the system of equations, we find the corners of the feasible region to be (0, 0), (0, 10), (5, 8), and (11, 0). arrow_forward Step 8 Evaluating the profit function at these points, we get P(0, 0) = 0, P(0, 10) = 500, P(5, 8) = 700, and P(11, 0) = 660. arrow_forward Step 9 Therefore, the profit is maximized at the point (5, 8), where 5 refrigerators and 8 stoves are produced for a total profit of $700. arrow_forward Solution The feasible solution space is the region bounded by the lines x + y = 13, 4x + 10y = 100, and 2x + y = 22. The profit is maximized at the point (5, 8), where 5 refrigerators and 8 stoves are produced for a total profit of $700.
graph the following :
Let's denote the number of refrigerators to be produced as 'x' and the number of stoves as 'y'. The profit
arrow_forward
Step 3
The constraints for the problem are as follows: - Assembly time: 4x + 10y <= 100 - Inspection time: 2x + y <= 22 - Storage space: 3x + 3y <= 39
arrow_forward
Step 4
We can simplify the storage space constraint to x + y <= 13 since both products require the same amount of storage space.
arrow_forward
Step 5
The feasible solution space is the set of values (x, y) that satisfy all the constraints. This is a region bounded by the lines x + y = 13, 4x + 10y = 100, and 2x + y = 22.
arrow_forward
Step 6
To find the point that maximizes the profit, we need to evaluate the profit function at the corners of the feasible region. These corners are the points where the constraint lines intersect.
arrow_forward
Step 7
By solving the system of equations, we find the corners of the feasible region to be (0, 0), (0, 10), (5, 8), and (11, 0).
arrow_forward
Step 8
Evaluating the profit function at these points, we get P(0, 0) = 0, P(0, 10) = 500, P(5, 8) = 700, and P(11, 0) = 660.
arrow_forward
Step 9
Therefore, the profit is maximized at the point (5, 8), where 5 refrigerators and 8 stoves are produced for a total profit of $700.
arrow_forward
Solution
The feasible solution space is the region bounded by the lines x + y = 13, 4x + 10y = 100, and 2x + y = 22. The profit is maximized at the point (5, 8), where 5 refrigerators and 8 stoves are produced for a total profit of $700.
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