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Profit is Shs. 3000 on a ring and Shs. 1900 on a chain. With $x$ rings and $y$ chains, the objective function to maximise is:
A$f(x,y)=1900x+3000y$
B$f(x,y)=3000x-1900y$
C$f(x,y)=4900(x+y)$
D$f(x,y)=3000x+1900y$
Answer & Solution
Correct answer: D. $f(x,y)=3000x+1900y$
1. The objective function totals the profit earned across both products.
2. Rings contribute $3000$ shillings each, so $3000x$.
3. Chains contribute $1900$ shillings each, so $1900y$.
4. Adding gives $f(x,y)=3000x+1900y$, to be maximised.
5. The version reading $1900x+3000y$ attaches each rate to the wrong product, and $4900(x+y)$ assumes a ring and a chain are always made together.
_Source: NECTA ACSEE 2023 Advanced Mathematics 142/1, Question 3: Linear Programming_
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