You cannot do the required calculations with the information that you have to hand. However, apart from ruling out completely pointless combinations of enzyme and substrate using theory, you really need to do experiments to find the best conditions. There are many reasons for this, but two important ones are that (i) the activity values may have been determined using assay conditions different from the ones that you will use (ii) the enzyme may not be as active as at the time of production.

I'll deal with enzyme and substrate separately. First, the enzyme - the value for enzyme that you have is specific activity, not enzyme activity (which is units/ml). The latter is far more useful in the context of assays, as it changes with dilution. Your units/mg is constant. So what you need to find here is the dilution of the enzyme to turn over an 'appropriate' amount of substrate. What is appropriate is governed by the need to generate a detectable assay signal and, ideally, not to convert more than 10-15% of substrate into product (which is important if you need to determine any kinetic parameters). The simplest way to find out the right amount of enzyme is to make serial dilutions and see how much product is formed in each case. Do large steps initially, 1/10; 1/100; 1/1000 and so on. Once you know roughly the right dilution, you can fine tune the dilution in a second experiment.

Substrate - I would convert these mg/ml amounts into molar terms (or mM or uM, as you prefer) as all kinetic work requires an understanding of moles of substrate converted. It would be helpful if you had the kinetic parameters of the enzyme, as some of the substrate concentrations may not be useful, but it depends what you are trying to do here. As you are looking at a range of concentrations it may be that you are trying to determine the kinetic parameters. As noted earlier, whatever the substrate concentration used, only a small proportion should be converted into product. This becomes challenging at very low substrate concentrations as there is also a need to generate a measurable assay signal. Some compromise is sometimes needed.

However, I would not worry too much about the kinetic 'rules' initially, just focus on getting a signal using serial dilutions of the enzyme with perhaps one concentration of substrate (medium to high). Once you have a signal, you have something to work with and then can explore the other lower/higher substrate concentrations. It is difficult to predict how product formation will vary with substrate concentration in your case, as you do not have a Km value.

Assuming you have the product available to create a standard curve, you can determine exactly how much substrate has been converted in each reaction. From there, you can calculate activity, specific activity, Km, Vmax etc.

In addition to what Nick Gee wrote above, it is necessary to know that the best combination to be used is not a universe, it is something you have trey yourself by doing several trials where you take different amounts of the enzyme with fixed substrate concentration and the other way around keeping in your mind what Nik Gee advice you to do. The other thing is if there are some previous studies dealing with the same enzyme, you can benefit from these literatures and try what they have achieved.

Good luck

The amount of enzyme and the substrate mainly depends on the type of assay you are going to perform or the method being utilized to detect the end product. We usually determine the product concentration produced in the reaction mixture.

The substrate concentration must be in the range (lower range) so that it do not produce any unwanted background in the final assay and must not be as high as it will hinder the activity of the enzyme as high concentrations of substrates are also known to hinder the catalytic performance of the enzymes. The standard recommended concentration usually can be found in the literature.

And the amount of enzyme to be used in the assay must be in the range so that it will produce the end product in the detectable range of your assay. Like if your end product is glucose in the assay and you are going to use DNS analysis (Miller, 1959; doi.org/10.1021/ac60147a030); prepare a glucose standard and the reading falling under your detectable range must also be used to calculate the assay end product concentration (glucose), and you must dilute the enzyme accordingly to produce the end product (glucose) in the detectable range.

Readings below the range== increase the enzyme concentration.

Readings above the detectable range== dilute the enzyme.