Write three to five sentences explaining which levels of production provide Alonzo’s Cycling with the maximum profit.
2 answers:
Answer:
The maximum profit can be attained when 4 bikes are produced each day.
Step-by-step explanation:
Look at the attached picture:
In the table given in the picture, the number of bikes produces varies. We cannot properly compare the profits per day. To be consistent, let us determine the profit per unit of bike produced.The relationship between cost, revenue and profit can be as:
Profit = Revenue - Cost
To find the profit per unit of bike, simply divide the profit with the number of bikes produced (1st column). After you see the results, we can see that the highest profit is $17.5 per unit of bike produced. Therefore, the maximum profit can be attained when 4 bikes are produced each day.
You might be interested in
Lagrange multipliers:
(if 
)
(if )
(if 
)
In the first octant, we assume
, so we can ignore the caveats above. Now,
so that the only critical point in the region of interest is (1, 2, 2), for which we get a maximum value of
.
We also need to check the boundary of the region, i.e. the intersection of
with the three coordinate axes. But in each case, we would end up setting at least one of the variables to 0, which would force 
, so the point we found is the only extremum.
In the first octant, we assume
so that the only critical point in the region of interest is (1, 2, 2), for which we get a maximum value of
We also need to check the boundary of the region, i.e. the intersection of