Question

One is able to use Gin (G) and Vermouth (V) to produce martini. A regular martini is produced with 2 portions Gin for 1 portion Vermouth. A dry martini is produced with 5 portions Gin and 1 portion Vermouth. The prices of a regular martini (PM) and a dry martini (PD) are fixed. You have a given supply to both Gin (G) and Vermouth (V).

a) what are the prices of Gin and Vermouth, i.e. WG and WV? You can think of these prices as analogs of the wages for labor and rental rate for capital. Hint WG and WV should be expressed as equations written in terms of PM and PD.

Answer 1

one regular martini takes 2 portions of (G) and 1 portion of (V), i.e 2:1

Quantity of gin used to make one unit of M = 2/3

Quantity of (V) used to make one unit of M = 1/3

PM = (2/3)*Wg + (1/3)*Wv - eq(1)

Similarly,

To make one unit of dry martini(D)

5/6 units of (G) and 1/6 units of (V) is used

PD = (5/6)*Wg + (1/6)*Wv - eq(2)

Solving eq 1 and 2 together,

3PM = 2 Wg + Wv

6PD = 5 Wg + Wv

After subtracting first from the second,

3Wg = 6PD - 3PM

WG =2PD - PM

and

WV = 3PM -2(2PD - PM)

WV = 5PM - 4PD.

Hope the answer helped you :)