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Answer :
Final answer:
The optimal solution is to make 150 yellow cakes and 0 strawberry cakes. The maximum revenue that can be generated is $5250.
Explanation:
To maximize revenue, we need to find the optimal combination of yellow and strawberry cakes based on the available labor hours and the time required for each type of cake.
Let's assume that x represents the number of yellow cakes and y represents the number of strawberry cakes.
Since the decorating assembly time required for the yellow cake is 2 hours and the time for the strawberry cake is 3 hours, the total labor hours required can be expressed as:
2x + 3y ≤ 450
Furthermore, we know that the bakery can make at most 150 yellow cakes, so:
x ≤ 150
Now, let's consider the revenue. The revenue from selling yellow cakes can be calculated as 35x, and the revenue from selling strawberry cakes can be calculated as 25y. Therefore, the total revenue can be expressed as:
R = 35x + 25y
Our goal is to maximize the revenue, so we need to find the maximum value of R.
To solve this problem, we can use linear programming techniques. By graphing the feasible region determined by the constraints, we can find the corner points of the region. We evaluate the objective function at each corner point and choose the one that gives the maximum revenue.
However, in this case, we can see that the maximum number of yellow cakes that can be made is 150, which is less than the total labor hours available. This means that the constraint 2x + 3y ≤ 450 will not be binding. Therefore, we can ignore this constraint and focus on maximizing the revenue.
Since the revenue is directly proportional to the number of cakes sold, we want to maximize the number of cakes sold. In this case, we can maximize the number of yellow cakes since they have a higher selling price. Therefore, the optimal solution is to make 150 yellow cakes and 0 strawberry cakes.
The maximum revenue can be calculated as:
R = 35(150) + 25(0) = $5250
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