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Answer :
The maximum revenue is $987, and it occurs when the company produces 141 kg of the second mix and 0 kg of the first mix.
Corner point (0, 81): R = 7x + 5y = 7(0) + 5(81) = 405
Set up variables
Let x be the number of kilograms of the first mix (half nuts and half raisins) that the company produces. Let y be the number of kilograms of the second mix (nuts and raisins) that the company produces.
We want to maximize the revenue, which is the total amount of money earned by selling the mixes. So, we need to express the revenue in terms of x and y and then find the values of x and y that maximize the revenue.
Step 1: Rewrite the revenue function
The revenue from selling the first mix is still 7x dollars, but the revenue from selling the second mix is now 11y dollars (since it sells for $11 per kg).
Therefore, the total revenue is R = 7x + 11y dollars.
Step 2: Rewrite the constraints
The constraints are still the same: x/2 + y/2 ≤ 141 and x/2 + y/2 ≤ 81.
Step 3: Draw the feasible region
The feasible region is still the same, so we can use the same graph:Graph of the feasible region for the chocolate mix problem
Step 4: Find the corner points of the feasible region
The corner points are still the same: (0, 81), (141, 0), and (54, 54).
Step 5: Evaluate the revenue function at the corner points
Corner point (0, 81): R = 7x + 11y = 7(0) + 11(81) = 891
Corner point (141, 0): R = 7x + 11y = 7(141) + 11(0) = 987
Corner point (54, 54): R = 7x + 11y = 7(54) + 11(54) = 756
The maximum revenue is $987, and it still occurs when the company produces 141 kg of the second mix and 0 kg of the first mix.
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