Competition among fitness clubs in Hong Kong is quite fierce, and this has led the clubs to offer a series of additional features and products in order to provide their customers with an integrated fitness and well-being experience.

As a result, registered club members will not only have access to a variety of sport and fitness facilities, but also to spa services, dietary products, and specialized doctors.

One branch of California, one of the first fitness clubs in Hong Kong, has decided to advertise a new diet that is free for its gold membership customers. It promises that its members will be able to pick up their favorite foods and combine them in the best way for both nutritional requirements and costs.

After having checked food availability, you decide that you want to pick up your preferred meal, which is salmon and chickpeas.

Here is the nutritional table for each serving.

Portion (grams/serving)

Nutritional Info Salmon Chickpeas Protein 20 5 Carbohydrates 5 15 Fat 15 2 Other constraints also need to be considered before deciding the best allocation in terms of cost.

First, the daily requirement for an adult of each food component, which has to be represented in the perfect combination, is as follows:

●● Protein should reach at least a value of 40 units in the total intake

●● Carbohydrates, at least 50

●● Fat, on the other hand, no more than 60 Second, the cost of the portion also has to be included in the table.
Considering all of these elements and knowing that a portion of salmon will cost 50 HKD and one of chickpeas will cost 35 HKD, you will need to:

a. Write a linear programming model, indicating variable and constraints.

b. Find a graphical solution.
Use Excel Solver or other software to determine the solution that minimizes the costs for the company. LO.1