quantitaive analysis help.

freeze4real

Hello guys i have Quants exam tomorrow and I'm stuck on this question.


I am thinking thats it has ro do with diffferntiation, but I'm not so sure.
Can somebody please go through the steps with me.



Firm oxynav considers getting a caterpillar for its construction operations.
Firm oxynav has the choice of leasing a caterpillar from a specialised leasing company or buying a caterpillar outright.
If firm oxynav leases the caterpillar, it will have to pay a leasing charge of 10 currency units, plus 0.1 currency units every time it uses the caterpillar (the specialised leasing company takes care of all the other costs of the caterpillar).
If oxynav decides to buy the caterpillar, the total cost of the caterpillar (expressed in currency units) will follow the function f(x) = 5 + 0.02x2 where x is the number of times that firm oxynav uses the caterpillar.
(a)
For the leasing option, derive the equation representing the total cost of the caterpillar as a function of the number of times that firm oxynav uses the caterpillar.
(b)
Graph the equation obtained in part (a), as well as the total cost equation for the purchase option, in one diagram.
(c)
Suppose firm oxynav knew in advance that it would have to use the caterpillar more than 50 times this year. Which option (lease or buy) would you advise the firm to use? Explain your answer

Anonymous1987

freeze4real wrote: »

Hello guys i have Quants exam tomorrow and I'm stuck on this question.


I am thinking thats it has ro do with diffferntiation, but I'm not so sure.
Can somebody please go through the steps with me.



Firm oxynav considers getting a caterpillar for its construction operations.
Firm oxynav has the choice of leasing a caterpillar from a specialised leasing company or buying a caterpillar outright.
If firm oxynav leases the caterpillar, it will have to pay a leasing charge of 10 currency units, plus 0.1 currency units every time it uses the caterpillar (the specialised leasing company takes care of all the other costs of the caterpillar).
If oxynav decides to buy the caterpillar, the total cost of the caterpillar (expressed in currency units) will follow the function f(x) = 5 + 0.02x2 where x is the number of times that firm oxynav uses the caterpillar.
(a)
For the leasing option, derive the equation representing the total cost of the caterpillar as a function of the number of times that firm oxynav uses the caterpillar.
(b)
Graph the equation obtained in part (a), as well as the total cost equation for the purchase option, in one diagram.
(c)
Suppose firm oxynav knew in advance that it would have to use the caterpillar more than 50 times this year. Which option (lease or buy) would you advise the firm to use? Explain your answer

For part a you are given a once off cost 10 and a per unit cost 0.1, hence the equation can be derived by constructing the function f(x) = 10 + 0.1(x) where x is the number of units used.
To graph the equations throw in values for x e.g. 0, 10, 20, 50, solve and plot on a graph drawing a line or curve (whichever fits best) through which matches the points for each equation.
From looking at the graph in (b) this should be obvious, otherwise just extend the lines already drawn until they intersect. Your explanation could say that lower variable costs in one equation mean that it is the least costly option at high per unit rates of 50 or more otherwise lower per unit rates would make the option with the lower fixed cost less costly overall.

freeze4real

Thanks alot for the solution.