# 10.6.3. Linear Programing and Optimization

A candy shop sells marshmallows and cola candies; the price of a marshmallows bag is LE, and that of a cola candy bag is LE. Determine the least cost at which the kid can buy from the 2 types using the figure below showing the restrictions of the situation, knowing that represents the amount of marshmallow bags, and represents that of cola candy bags.

• ALE
• BLE
• CLE
• DLE

### Example

A candy shop sells marshmallows and cola candies; the price of a marshmallows bag is LE, and that of a cola candy bag is LE. Determine the least cost at which the kid can buy from the 2 types using the figure below showing the restrictions of the situation, knowing that represents the amount of marshmallow bags, and represents that of cola candy bags.

### Solution

Since the price of a marshmallows bag is LE, the total price of all marshmallows bags is LE, and since the price of a cola candy bag is LE, the total price of all cola candy bags is LE. Therefore, if the total price of all the candy bags is , the objective function is . The vertices of the feasible region are , , and . First, find the value of the objective function at the vertex .

Next, find the value of the objective function at the vertex .

Finally, find the value of the objective function at the vertex .

Thus, finding the value of the objective function at each vertex shows that the minimum value of the function is LE, so this is the smallest amount a kid could spend on the two types of candy bags.

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