CODEWITHSUNDEEP
pythonpython-3.x
Chelsea Lewis
Chelsea Lewis

Reputation: 257

How to find the ideal price for a product (provides highest profit) by searching a range of prices

def profit():
    price = input('Enter a price: ')
    demand = 650 - (10 * price)
    cost_per_item = 35
    firm_profit = (price - cost_per_item) * demand
    return firm_profit

How can one search through a range of prices to find the price that provides the highest profit based on this relationship between demand and the product?

Upvotes: 3

Views: 654

Answers (3)

gboffi
gboffi

Reputation: 25023

Another possibility: first define a demand function, next a profit function and eventually use the max builtin applied to a generator expression that produces couples of values (profit, price) that max, by default, compares taking into account the first value in the couple.

>>> def demand_01(price):
...    return 650-10*price
>>> def profit(price, cost, demand):
...    return (price-cost)*demand(price)

>>> print(max((profit(price, 35, demand_01), price) for price in (39.95, 69.90, 99.00))
(1239.9750000000008, 39.95)

The advantage of definining separately a demand and a profit function and using max lies in

  1. the possibility of using whatever mathematical definition (even piecewise), w/o involving the differentiability of the profitfunction and
  2. the possibility of definining different demand functions to explore the sensitivity of the results on different assumptions.

Addendum

To have the best price and the associated maximum profit you can unpack the result returned by the max builtin:

max_profit, best_price = max( (profit(price, 35, demand_01), price)
    for price in (...))

Upvotes: 1

AGN Gazer
AGN Gazer

Reputation: 8378

It is really a mathematical problem. Your formula for profit is:

profit = (p - c) * d = (p - c) * (650 - 10 * p)

where I abbreviated p for price, c for cost_per_item, d for demand.

To maximize profit all that you need to do is to find the value of p for which derivative of profit with regard to p is zero:

d(profit) / d(p) = 650 + 10*c - 20*p = 0 =>
pmax = (650 + 10*c) / 20

If you need to pick a price from a list of possible values, pick the one closest to pmax (since profit is a parabola with regard to p and so it is symmetric around the vertical line passing through pmax).

Therefore, if you do have a list of prices (I suppose this is what you mean by "range of values") contained in a list prices, then:

best_price = min(abs(x - pmax) for x in prices)

where pmax was computed earlier.

Upvotes: 1

Alfred Brewer
Alfred Brewer

Reputation: 26

If this problem uses discreet units (for example, if you must use integers) then you just use a loop to try every possibility from a price of 0 to a price which would produce a zero demand (65 in this case, because 650 - 10*65 = 0).

I would start by moving the price from an input to a parameter of the function, so:

def profit(price):
     demand = 650 - (10 * price)
     cost_per_item = 35
     firm_profit = (price - cost_per_item) * demand
     return firm_profit

Then we define a variable to pass through the function and increment it to try every possibility:

price = 0
best_price = 0
increment = 1
while price<65:
    if profit(price)>profit(best_price):
        best_price = price
    price += increment

If you end up needing to use a decimal increment, you might want to use the decimal module to avoid some strange, floating point behavior.

Upvotes: 0

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