Question

The following questions are based on this problem and accompanying Excel windows. Jack's distillery blends scotches for local bars and saloons. One of his customers has requested a special blend of scotch targeted as a bar scotch. The customer wants the blend to involve two scotch products, call them A and B. Product A is a higher quality scotch while product B is a cheaper brand. The customer wants to make the claim the blend is closer to high quality than the alternative. The customer wants 50 1500 ml bottles of the blend. Each bottle must contain at least 48% of Product A and at least 500 ml of B. The customer also specified that the blend have an alcohol content of at least 85%. Product A contains 95% alcohol while product B contains 78%. The blend is sold for $12.50 per bottle. Product A costs $7 per liter and product B costs $3 per liter. The company wants to determine the blend that will meet the customer's requirements and maximize profit

Answer 1

A blend of two scotch products, A and B, is to be optimized for profit while adhering to certain quality and cost constraints. The ideal ratio must satisfy product quality, volume, and alcohol content preferences of the customer and maximize the profit per bottle sold.

Step-by-step explanation:

The student's question is centered around a business problem involving the blending of two scotch products, A and B, to meet certain quality, content, and cost requirements for a customer. In this case, the objective is to determine the optimal blend of the two products to maximize profit while satisfying the customer's conditions regarding product quality (at least 48% of Product A), quantity (at least 500 ml of Product B per bottle), and alcohol content (at least 85%). Product A has a 95% alcohol content and costs $7 per liter, while Product B has a 78% alcohol content and costs $3 per liter. The selling price of the blend is $12.50 per bottle.

To solve this problem, we can use a linear programming approach or set up a system of equations considering the constraints and the profit function. The solution would give us the exact blend ratio of products A and B that maximizes profit under the given constraints.

Answer 2

The blend should be made with 720 ml of Product A and 780 ml of Product B

Step-by-step explanation:

We create excel solve to get the cheapest blend with the requirement givens by the customer:

A B C D E F

1 ml type $ alcohol $mix alcohol mix

2 720 Product A 7 0.95 5.04 0.456

3 780 Product B 3 0.78 2.34 0.4056

4 Total 7.38 0.8616

5 Sales Price 12.50

6 Gross Profit 5.12

Constrains:

A2 = integer

A2 > 1500 x 48/100

A3 > 500

F4 > 0.85