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Food Factory is Making a Beverage for a Customer From Mixing
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Assignment Task
Questions
1. A food factory is making a beverage for a customer from mixing two different existing products A and B. The compositions of A and B and prices ($/L) are given as follows,
| Sales | Price | Production | Cost | Purchase Price |
| Spring | $60 | $5 | $30 | Cotton |
| Autumn | $55 | $3 | $45 | Wool |
| Winter | $60 | $5 | $50 | Silk |
2.Explain why a linear programming model would be suitable for this case study.
| Demand | Min Cotton proportion | Min Wool proportion | |
| Spring | 3300 | 55% | 30% |
| Autumn | 3600 | 45% | 40% |
| Winter | 4000 | 30% | 50% |
3. Formulate a Linear Programming (LP) model for the factory that minimizes the total cost of producing the beverage while satisfying all constraints.
4. Use the graphical method to find the optimal solution. Show the feasible region and the optimal solution on the graph. Annotate all lines on your graph.
5. What is the range for the cost ($) of A that can be changed without a↵ecting the optimum solution obtained above.
6. A factory makes three products called Spring, Autumn, and Winter, from three materials containing Cotton, Wool and Silk. The following table provides details on the sales price, production cost and purchase cost per ton of products and materials respectively.
7. The maximal demand (in tons) for each product, the minimum cotton and wool proportion in each product is as follows:
8. Formulate an LP model for the factory that maximises the profit, while satisfying the demand and the cotton and wool proportion constraints. There is no penalty for the shortage.
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