Question

2. To make the perfect Singapore Sling (a fancy cocktail) requires 1 oz gin, G 2 oz ice, I 4 oz orange juice, O 1 oz lime juice, L 1/2 oz grenadine, D The bar has 60 oz gin, 120 oz orange juice, 40 oz lime juice, 20 oz grenadine and unlimited ice. a) What is the bar's production function for a Sling? b) What is the maximum number of Slings that can be produced?

Answer 1

a)Let a Singapore sling be denoted as S.

Production function shows the proportion of every input used to make a single unit of output.

Here the inputs are gin(G), Ice(I), orange juice (o), lime juice (L), grenadine (D) and the output is a Singapore sling(S).

So the production function will be

S = G + 2I + 4O + 1L + (1/2)D

b)It is given that the bar has 60 oz gin , 120 oz orange juice, 40 oz lime juice, 20 oz grenadine and unlimited ice.

So ice will be never be a constraint for us as it unlimited.

If we take gin as a constraint then the maximum we can produce is (60/1) = 60 Singapore sling.

If we take orange juice as a constraint then the maximum we can produce is (120/4) = 30 Singapore sling.

If we take lime juice as a constraint then the maximum we can produce is (40/1) = 40 Singapore sling.

If we take grenadine as a constraint then the maximum we can produce is (20/.5) = 40 Singapore sling.

As everything is required in exactly given proportions, the maximum Singapore sling that can be produced will be determined by the least possible production permitted by the different constraints.

So according to this, we can see that we can produce a maximum of 30 Singapore sling.