Answer: 4
Step-by-step explanation:
Let N be the total number of runs.
The microscopes per year will be equal to the total number of runs * microscopes per run
total number of microscopes = total number of runs * microscopes per run
now we have each run to cost 2500, therefore:
run costs = 2500 * total runs = 2500*N
we also have insurance and storage costs (note the average thats why we divide by 2):
storage costs = 20* microscopes per run /2 = 20*N/2
insurance costs = 15 * microscopes per run = 15*N
the costs are:
costs = run costs + storage + insurance
now the comany sells 1600 microscopes a year, so in order to figure out the number of microscopes per run we divide 1600 by the total number of runs N and replace in the costs
costs = 2500N + 40000/N => C(N) = 2500N + 40000/N
now derivate the function with respect to N and equal to 0:
this gives you two solutions, N = -4 which is not eligible (you cant make negative microscopes lol) and N = 4 which is the answer
have a nice day
