Question

A patient consults a doctor at Levy Mwanawasa Hospital to check up his ill health. The doctor examination advises him to consume vitamin A and D regularly for a period of time so that he can regain his health. Doctor prescribes tonic 𝑇1 and tonic 𝑇2 which are having vitamins A and D in certain percentages. The doctor also advises the patient to consume at least 4 units of vitamin a and 5 units of vitamins D daily. The cost of tonics 𝑇1 and 𝑇2 and the proportion of vitamin A and D that are present in 𝑇1 and 𝑇2 are given in the table below.

Vitamins

Tonics

Daily Requirement

𝑻𝟏

𝑻𝟐

𝐴

1

2

4

𝐷

1.5

1

5

Cost in kwacha per unit

1.5

1.25

(a) Formulate LPP to minimize the cost of the tonics.

[4 marks]

(b) Solve the LPP and interpret your results