Question

A chocolate manufacturing company produces two types of chocolate: A and B. Ingredients required for manufacturing the products include milk and cacao only . Each unit of type A chocolate requires 2 units of milk and 4 units of cacao. Each unit of type B chocolate requires 1 units of milk and 3 units of cacao. The company's production plant has a total of 22 units of milk and 46 units of cacao available. On each sale the company makes a profit of $6.20 for every unit of chocolate of type A and $4.20 for every unit of type B. Develop a linear programming model to determine the manufacturing quantity for each type in order to maximize profit..

Answer 1

Answer:

The maximum profit is when they make 10 units of A and 2 units of B.

Step-by-step explanation:

Let x is units of milk

Let y units of cacao

Given that :

The company's production plant has a total of 22 units of milk and 46 units of cacao available.

2x + y ≤ 22 (2 unit of milk for each of A and 1 for B; 22 units available)

4x + 3y ≤46 (4 unit of milk for each of A and 3 for B; 46 units available

Graph the constraint equations and find the point of intersection to determine the feasibility region.

The intersection point (algebraically, or from the graph) is (10, 2)

The objective function for the problem is the total profit, which is $6.2 per unit for A and $4.2 per unit for B: 6.2x + 4.2y.

Hence, we substitute (10, 2)  into the above function:

6.2*10 + 4.2*2 = 70.4

The maximum profit is when they make 10 units of A and 2 units of B.