sorry here again..
never mind the table i said...sorry
The cheesy company produces two types of cheese with extra sharp cheddar cheese. The cheese spreads are packaged in 120 ounce containers, which are then sold to distributors throughout northeast. The regular blend contains 80% mild cheddar and 20% extra sharp, and Zesty blend contains 60% mild cheddar and 40% extra . This year, a local diary cooperative has offered to provide up to 8100 pounds of extra sharp cheddar cheese for $80 per pound. The cost to blend and package the cheese spreads, excluding the cost of the cheese, is %10 per container,If each container of regular is sold for $1000 and each container of Zesty should the New England produce?Formulate the LP, Solve it using graphical method and then interpret the result
thank you very much
OK, do it graphical as I stated, with the axis I suggested.
To solve this problem using linear programming and the graphical method, we need to define the decision variables, objective function, and constraints.
Decision Variables:
Let R represent the number of containers of regular blend cheese spreads to produce.
Let Z represent the number of containers of zesty blend cheese spreads to produce.
Objective Function:
We want to maximize the profit, which can be calculated as the revenue minus the cost, for New England Produce.
The revenue is the sum of the selling prices of regular and zesty blends:
Revenue = (Selling price per container of regular blend) * R + (Selling price per container of zesty blend) * Z
The cost is the sum of the costs of production, packaging, and the cost of cheese:
Cost = (Cost to blend and package per container) * (R + Z) + (Cost per pound of cheese) * (Weight of extra sharp cheddar cheese used)
Thus, the objective function can be defined as:
Maximize: Profit = Revenue - Cost
Constraints:
1. The weight of extra sharp cheddar cheese used should not exceed the available supply from the local dairy cooperative:
(Weight of extra sharp cheddar cheese used) = (Weight of extra sharp cheddar cheese in regular blend) * R + (Weight of extra sharp cheddar cheese in zesty blend) * Z <= 8100 pounds
2. Non-negativity constraint:
R >= 0 and Z >= 0
With the problem defined above, we can solve it using the graphical method. First, draw the feasible region for the constraints. Then, find the corner points of the feasible region and calculate the corresponding profit for each corner point. The corner point with the highest profit will give us the optimal solution.
Interpreting the result:
The optimal solution will tell us the number of containers of regular blend cheese spreads (R) and zesty blend cheese spreads (Z) that New England Produce should produce in order to maximize their profit. We will also be able to determine the maximum profit that can be achieved.
Note: Some values and parameters are missing from the original problem description (e.g., selling price per container, cost per container, weights of cheddar cheese in the blends). Please provide those missing values to obtain a numerical solution.