a) You are considering producing two types of drink: Original and Venti, both of which consist solely of milk, cream cheese, and coffee
At present, you have in stock
The mixture used to make Venti must contain at least 20% cream cheese.
The mixture used to make Original must have at least 10% cream cheese and 10% milk.
Both types of coffee must have at least 50% coffee.
Each ounce of Venti can be sold for 25¢ , and each ounce of Original for 20¢. Formulate an LP that will enable you to maximize your revenue from coffee sales.
b) Your partner Jane suggests that the selling price of your product should change according to the demand at different times of the year. She approximates that the selling price should increase by 10% in the fourth quarter of the year, and decrease by 20% in the second quarter of the year. Assume her approximations are accurate and you can solve the LP as often as you want, explain how would you change your current approach in part (a) to accommodate her suggestions. How much would these adjustments change the optimal solution and why?
To maximize revenue from coffee sales, we can use linear programming (LP) to find the optimal quantities of Original and Venti drinks to produce. Let’s define the decision variables:
The objective is to maximize the revenue, which is the sum of the revenues from Venti and Original: Maximize 0.25�+0.20�
Now, let’s set up the constraints based on the available resources and the composition requirements:
The final LP can be summarized as follows: Maximize 0.25�+0.20� Subject to: �+�≤100 0.20�≤20 0.10�≤20 0.10�≤30 �−0.50�−0.50�≥0
Incorporating Jane’s suggestion to adjust prices based on the demand at different times of the year requires modifying the objective function to account for varying prices. Let � represent the price multiplier:
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