(a) TC(x) = 20x, D(P) = 50(30 – P) = 1500 - 50P or P = 30 - Q/50. Assume the distributor’s costs are zero and you are charging your distributor a single price W per mask.
In this case the price W you charge your distributor is not higher than profit per unit sold.
The price P and the quantity of masks x are:
X is optimal at MR = MC.
MR = TR' = (P*x)' = 30 - x/25,
MC = TC' = 20,
30 - x/25 = 20,
x = 250 units,
P = 30 - 250/50 = 25.
The profits are:
TP = TR - TC = 25*250 - 20*250 = 1250