Assume you have some 135 lb. hogs on feed and would like to have them gain another 130 lbs. before they are sold. Research has shown that any one of the following combinations of corn and soybean oil meal (SBOM) will put 130 lbs. of gain on a 135 lb. hog. Your problem is to find the combination (i.e., Ration Number) which will put on the gain for the least cost. Complete the table and answer the questions which follow.
|
Ration Number
|
Corn (lbs.)
|
SBOM (lbs.)
|
Substitution Ratio
|
|
#1
|
421.2
|
35
|
XXX
|
|
#2
|
395.7
|
40
|
|
|
#3
|
376.0
|
45
|
|
|
#4
|
360.5
|
50
|
|
|
#5
|
347.1
|
55
|
|
|
#6
|
335.8
|
60
|
|
|
#7
|
326.2
|
65
|
|
|
#8
|
317.5
|
70
|
|
|
#9
|
310.0
|
75
|
|
|
#10
|
303.8
|
80
|
|
1. For each price combination, compute the price ratio and find the corresponding least-cost ration.
Price Least-Cost
Ratio Ration No.
a) Corn at 4.0¢ per lb., SBOM at 12¢ per lb. _________
b) Corn at 5.7¢ per lb., SBOM at 7.5¢ per lb. _________
c) Corn at 5.0¢ per lb., SBOM at 9¢ per lb. _________
d) Corn at 6.5¢ per lb., SBOM at 14¢ per lb. _________
e) Corn at 3.0¢ per lb., SBOM at 15¢ per lb. _________
2. Is the least-cost ration really least-cost? Let's do one check. Using the prices in question #1a) above, figure the total cost of your least-cost ration for question #1a) and for Ration #8. How much money would you save by feeding your least-cost ration instead of Ration #8? SHOW WORK!
3. If corn costs 4.4¢ per lb., what would SBOM have to cost to make ration #6 the least-cost ration? SHOW WORK!
4. What happens to the least-cost ration if the price of both feeds doubles? WHY?
5. What would happen to the substitution ratios you have calculated if the corn values were all 10 lbs. higher? What would happen to the total cost of any of the least-cost rations?