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
A company makes two types of leather shoes, shoe A and shoe B. Shoe A is a high quality shoe and shoe B is a low quality. The respective net returns are K4 and K3 per shoe. The production of each of type A requires twice as much time as shoe of type B, and if all shoes were of type B, the company could make 1000 shoes per day. The supply of leather is sufficient for only 800 shoes per day (both B and B combined). Shoe A requires a fancy laces and only 400 of these are available per day. There are only 700 laces a day for shoes B.
(a) Formulate the LPP and state the assumption you made.
[5 marks]
(b) Determine the daily production of each type of shoe type. Use simplex method.
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