Homework SourseSteam Sales Physical stores hold sales in order to clear out
Steam Sales
Physical stores hold sales in order to clear out extra inventory and make up losses. However, with digital distribution platforms such as steam, because the cost of producing physical copies is eliminated, putting items on sale often has the upside-down effect of increasing both sales and profits.
Suppose a particular game on steam costs $20, and it is estimated that for, every $6 the price is reduced, monthly sales will double. Use optimization principles (and derivatives of exponential functions) to determine the exact discount that would maximize profits under this model.
Steam Sales
Physical stores hold sales in order to clear out extra inventory and make up losses. However, with digital distribution platforms such as steam, because the cost of producing physical copies is eliminated, putting items on sale often has the upside-down effect of increasing both sales and profits.
Suppose a particular game on steam costs $20, and it is estimated that for, every $6 the price is reduced, monthly sales will double. Use optimization principles (and derivatives of exponential functions) to determine the exact discount that would maximize profits under this model.
Steam Sales
Physical stores hold sales in order to clear out extra inventory and make up losses. However, with digital distribution platforms such as steam, because the cost of producing physical copies is eliminated, putting items on sale often has the upside-down effect of increasing both sales and profits.
Suppose a particular game on steam costs $20, and it is estimated that for, every $6 the price is reduced, monthly sales will double. Use optimization principles (and derivatives of exponential functions) to determine the exact discount that would maximize profits under this model.
Solution
let previous sales be y
after reducing price by 6x , sales become 2^x *y
we want to optimize Cost = (20 - 6x) * 2^x * y
y is some constant
differentiate w.r.t x and equate to zero
-6 (2^x *y) + (20-6x)* 2^x ln(2) *y = 0
gives
(20-6x ) ln2 = 6
20 - 6/ln2 = 6x
x = 10/3 - 1/ln 2
= 2.64
