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The New England Cheese Co. produces two cheese spreads by blending mild cheddar with extra sharp cheddar cheese. The cheese spreads are packaged in 128-oz containers, which are then sold to distributors.

- The Regular blend contains 80% mild cheddar and 20% extra sharp cheddar.
- The Zesty blend contains 60% mild cheddar and 40% extra sharp cheddar.

This year, a local dairy cooperative offered to provide up to 8,100 lbs of mild cheddar cheese for P54 per lb and up to 3,000 lbs of extra sharp cheddar cheese for P63 per lb. The cost to blend and package the cheese spreads, excluding the cost of cheese, is P9 per container.

If each container of Regular is sold for P700 and each container of Zesty is sold for P750, how many containers of Regular and Zesty should New England Cheese produce in order to maximize profit?

Answer :

Final answer:

To maximize profit, New England Cheese Co. should use Linear Programming to calculate the optimal quantities of Regular and Zesty spread to produce given the constraints of available cheeses and costs.

Explanation:

The problem involves the use of Linear Programming to determine the number of Zesty blend and Regular cheese containers to be produced to maximize the profit.

Firstly, note that 1 lb equals approximately 16 oz. The total quantity of mild cheddar available is 8,100 lbs (129,600 oz) and of extra sharp cheddar is 3,000 lbs (48,000 oz). Therefore, given the percentage of cheddar in each blend, we can form inequalities. For example, for the Regular blend, 0.8x <= 129,600 represents the mild cheddar, and 0.2x <= 48,000 represents the extra sharp cheddar.

To formulate the profit function, first calculate the cost per container (including the cheese purchase and packaging cost) and then subtract this from the selling price to get the profit per container. Plug in the quantities to get the equation for the profit function, P = 700x - Cost(x) + 750y - Cost(y).

Finally, the aim is to maximize P using the constraints gained from the inequalities above while keeping in mind that x, y >= 0 (you can't produce negative quantities). The solution to this problem would give you the optimal quantities of Regular and Zesty spread to produce to maximize profit.

Learn more about Linear Programming here:

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