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

no graph, just need a table...^^

What table? This is an ideal linear prog prob, mild on one axis, sharp on the other. There is a constraint on the extra sharp axis

The profit function is confusing, as the price for the regular is not given. I assume a typo in that part.

To formulate the linear programming (LP) problem, we need to define the decision variables, objective function, and constraints.

1. Decision Variables:
Let x1 represent the number of containers of Regular blend cheese spreads to produce.
Let x2 represent the number of containers of Zesty blend cheese spreads to produce.

2. Objective Function:
The objective is to maximize the profit.
The profit from selling each container of Regular blend is $1000, and each container of Zesty blend is $1500.
Maximize Z = 1000x1 + 1500x2 (Profit)

3. Constraints:
- Total pounds of extra sharp cheddar cheese available is limited to 8100 pounds.
80% of the Regular blend and 40% of the Zesty blend are made using extra sharp cheddar cheese.
0.8x1 + 0.4x2 <= 8100 (Cheese Constraint)

- The cost of blending and packaging per container is 10%.
The cost for each container is $100.
0.1(1000x1 + 1000x2) <= Total Cost (Cost Constraint)

- Non-negativity constraint:
x1 >= 0 (Non-negativity constraint for Regular blend)
x2 >= 0 (Non-negativity constraint for Zesty blend)

Now, let's graph the inequalities using a graphical method to find the feasible region and solve the LP problem.

Graphical Method:
Step 1: Rewrite the constraints in slope-intercept form:
- 0.8x1 + 0.4x2 <= 8100 can be rewritten as x2 <= (8100 - 0.8x1) / 0.4
- 0.1(1000x1 + 1000x2) <= Total Cost can be simplified to 100x1 + 100x2 <= Total Cost

Step 2: Plot the feasible region:
First, plot the line x2 = (8100 - 0.8x1) / 0.4.
Next, plot the line 100x1 + 100x2 = Total Cost.

Step 3: Identify the feasible region:
The feasible region is the region where all constraints are satisfied. It will be the area where the shaded region intersects.

Step 4: Determine the optimal solution:
Optimal solution can be found at the vertices (corners) of the feasible region. Calculate the profit (Z) at each vertex using the objective function. The vertex with the highest profit will be the optimal solution.

Interpretation:
The optimal solution will provide the quantities of Regular blend (x1) and Zesty blend (x2) to produce in order to maximize profit.

Please note that for the specific values of "Total Cost" and the coordinates of the vertices of the feasible region, the exact solution can be found. Without those values, we cannot provide the numerical solution at this time.

To formulate the linear programming problem, we need to define the decision variables, objective function, and constraints.

Decision Variables:
Let "x" represent the number of containers of the regular blend.
Let "y" represent the number of containers of the zesty blend.

Objective Function:
We want to maximize the total profit from selling the cheese spreads.
The profit from each regular container is $1000, and the profit from each zesty container is $1500.
Thus, the objective function can be written as:
Maximize: Profit = 1000x + 1500y

Constraints:
1. The total weight of extra sharp cheddar cheese used cannot exceed 8100 pounds. Considering the ratio of extra sharp cheddar in each blend, the constraint can be written as:
0.2x + 0.4y ≤ 8100

2. The amount of cheese used cannot exceed the availability provided by the local dairy cooperative. The cost to obtain the extra sharp cheddar cheese is $80 per pound. Therefore, the cost constraint can be written as:
0.2x + 0.4y ≤ 80 * (x + y)

3. The cheese spreads are packaged in containers, and the cost to blend and package each container is 10% of the selling price. The selling price of each container is $1000 for the regular blend and $1500 for the zesty blend. Therefore, the cost constraint can be written as:
0.1 * 1000x + 0.1 * 1500y ≤ 0.1 * (1000x + 1500y)

4. Since we are dealing with containers, the number of containers cannot be negative. Hence, the non-negativity constraint is:
x ≥ 0, y ≥ 0

Now, let's solve this linear programming problem using the graphical method.

First, plot the feasible region bounded by the constraints on a graph. Then, evaluate the objective function at each corner of the feasible region. The corner that maximizes the objective function will be the optimal solution.

The final interpretation will depend on the result obtained after solving the problem using the graphical method, so it cannot be provided in advance.