Question

A pig weighing 200 pounds gains 5 pounds per day and costs 45 cents a day to keep. The market price for pigs is 65 cents per pound, but is falling 1 cent per day. Do a sensitivity analysis of the time to wait to sell (denoted by t) to the keeping cost k. Derive a general expression of S ( t , k ) and evaluate it at k = 0.45 keeping all other constants the same, g = 5 , r = 0.01. Use words to explain .

P(t) for Profit

p(t) for price

w(t) for the weight of the pig

R(t) for the revenue from the sale

c(t) for the cost to keep the pig

g = 5 is the growth rate and r = 0.01 is the one cent each day

Answer 1

Pric=P(t)=65-t*1

p(t)=65-t

Weight=W(t)=200+5*t

W(t)=200+5t

Revenue=R(t)=Price*Weight=(65-t)*(200+5t)

R(t)=(65-t)*(200+5t)

Cost to keep the pig=c(t)=45t

Profit=P(t)=R(t)-c(t)

P(t) in Cents =(65-t)*(200+5t)-45t

P(t) in Pounds=(0.65-0.01t)*(200+5t)-kt

P(t)=130-2t+3.25t-0.05(t^2)-kt

P(t)=130+1.25t-0.05(t^2)-kt

t	R(t)	c(t)	P(t)	130+1.25t-0.05(t^2)-0.45t
Number of days	Revenue(Cents)	Cost(Cents)	Profit(Cents)	Profit(Pounds)
0	13000	0	13000	130
1	13120	45	13075	130.75
2	13230	90	13140	131.4
3	13330	135	13195	131.95
4	13420	180	13240	132.4
5	13500	225	13275	132.75
6	13570	270	13300	133
7	13630	315	13315	133.15
8	13680	360	13320	133.2
9	13720	405	13315	133.15
10	13750	450	13300	133
11	13770	495	13275	132.75
12	13780	540	13240	132.4
13	13780	585	13195	131.95
14	13770	630	13140	131.4
15	13750	675	13075	130.75
16	13720	720	13000	130

Profit will be maximum in 8 days

t=8

Profit=133.2