Question

Golden Harvest Foods makes jumbo biscuits and regular biscuits. The oven can cook at most 200 biscuits per day. Each jumbo biscuit requires 2 oz of flour, each regular biscuit requires 1 oz of flour, and there is 350 oz of flour available. The income from each jumbo biscuit is $0.10, and from each regular biscuit is $0.08. How many of each size biscuit should be made to maximize income?

Answer 1

To maximize income, Golden Harvest Foods must use linear programming to find the optimal number of jumbo and regular biscuits to bake, given the constraints of oven capacity (200 biscuits) and flour availability (350 oz). The income function to maximize is $0.10 per jumbo biscuit and $0.08 per regular biscuit.

Step-by-step explanation:

The question pertains to linear programming, a method used in mathematics to optimize a particular outcome given a set of linear constraints. Golden Harvest Foods must determine the number of jumbo and regular biscuits to bake in order to maximize income, while considering the constraints of oven capacity and flour availability.

Let's denote the number of jumbo biscuits as J and the number of regular biscuits as R. The constraints can be formulated as follows:

• The oven can bake at most 200 biscuits a day, so J + R ≤ 200.
• Each jumbo biscuit requires 2 oz of flour and each regular biscuit requires 1 oz of flour, so 2J + R ≤ 350 (since only 350 oz of flour is available).

The income from each jumbo biscuit is $0.10, and from each regular biscuit is $0.08, thus the income function to maximize is 0.10J + 0.08R.

Using these equations, Golden Harvest Foods would use linear programming techniques, such as simplex algorithm or graphical methods, to find the optimal solution for J and R that maximizes income.