finding the quantities of each type of dog treats to be produced for maximum profit of Petopia Ltd as a linear programming problem

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

QUESTION 1: (20 MARKS)

Petopia Ltd produces two types of dog treats namely Camilove and Camilove Plus, which are sold on the Mauntian marloet m loo gram sachet. Three types of vitamins (Vi, V2 and V3) are used to produce these two dog food. Camilove requires 12, 4. and 2 grams respectively of the three types of vitamins. Camilove Plus requires 6, 10 and 3 grams respectively of the three types of vitamins. The total available vitamins in

kilograms respectively is 6, 4, and 1.8. Camelove generate a prot of Rs 40 and Camilove Plus RslOO.

(a) Summarize this information m the form of a table. (1 mark)

(b) Formulate the problem of finding the quantities of each type of dog treats to be produced for maximum profit of Petopia Ltd as a linear programming prOblem. Take care in your answer to define the decision variables and to explain briefly how the objective function and the constraints are derived. (3 marks)

(C) Solve the linear programming problem obtained n (b) graphically. Shade me feasible region with a pencil. Hence find the optimal solution for this problem and the maximum profit for Petopia Ltd. (8 marks)

(d) Determine whether there are any unused resources at the optimal solutions, and by how much. (4 marks)

(e) Suppose Petopia Ltd has to produce at most 200 sachets of Camilove to meet suppliers demand. 

(i) What additional constraint must be added to the problem formulated in (b) to model this new problem? (1 mark)

(ii) Add the new constraint to the diagram and find the revised optimal solution. (3 marks)

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