Question

Genko Olive Oil Company has decided to diversify, and begin making and selling flour. It has decided to specialise in two types; bread flour and self-raising flour. Genko would like to determine how much of each type of flour it should pro- duce each day in order to maximise its profits. The profit made on the sale of 1 kg of bread flour is $2, while the profit made on the sale of 1 kg of self-raising flour is $1.80. The company is capable of making up to a total of 200 kg of flour per day. However, due to an ongoing shortage of baking powder (a key input in the production of self-raising flour) Genko can only produce up to 150 kg of the self-raising flour per day. In addition, company management are anticipating a high demand for self-raising flour (a key ingredient in cakes and puddings) as the holiday season approaches. For this reason, they have decided that the company should produce at least twice as much self-raising flour as bread flour.

(a) Formulate this problem as an optimization problem.

Answer 1

The optimization problem for Genko requires maximizing the objective function P = 2x + 1.8y, representing daily profit, subject to production and proportionality constraints. Here, x and y are the quantities of bread flour and self-raising flour produced, respectively.

Step-by-step explanation:

The optimization problem for Genko Olive Oil Company involves determining the optimal daily production quantities of bread flour and self-raising flour to maximize profits, given certain constraints. The profit from bread flour is $2 per kg, while self-raising flour yields $1.80 per kg.

The company can produce a total of up to 200 kg of flour per day but is limited to 150 kg per day for self-raising flour due to a baking powder shortage. Furthermore, there's a requirement that at least twice as much self-raising flour is produced compared to bread flour.

To formulate this as a linear programming problem, we let x represent the quantity of bread flour and y represent the quantity of self-raising flour produced per day. The objective function to be maximized is the daily profit, P = 2x + 1.8y. The constraints are x + y ≤ 200 (total production limit), y ≤ 150 (self-raising flour limit), and y ≥ 2x (at least twice as much self-rising flour as bread flour).