Simple Marketing Budget Optimisation

This tool maximises output given a marketing spend function. The function should take the shape

such that total spend is constant. We use the function
,
where Y is output and x are the marketing channels, a, b and c are estimated parameters. You need to estimate these parameters in Excel, SAS, R or similar software. The ln() function ensures diminishing returns.
Total budget
a constant
b channel 1
c channel 2
d channel 3
e channel 4
f channel 5

Parameters b-f need to be positive.
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