A pharmaceutical firm is evaluating three potential locations for a new production plant. The first location is in a rural setting, the second in an urban setting, and the third in a suburban setting. The corporation has calculated that land and construction costs will be same at all three locations. Additionally, the corporation has assessed that both the urban and suburban locations would need the same level of expenditure in security and environmental protection. The corporation has determined that the rural location is the greatest alternative since it is the least costly and has the least danger of environmental pollution and criminal activity.
In Indianapolis, both the unit cost and Machine time per pound of each medicine are cheaper. Therefore, we will create the medication first in Indianapolis, which offers larger hourly savings, as calculated below:
Drugs 1 2
Savings in cost 0.20 0.50 (4-3.8; 5.2-4.7)
Machine Time 0.20 0.30
Savings per hour 1 1.6667
So we will first produce Drug 2 in Indianapolis, time required = 3000 * 0.30 = 900 hours
But we have only 800 hours in Indianapolis, so we can produce = 800 / 0.30 = 2666.67 units
Balance (3000 – 2666.67) 333.33 units of drug 2 will be produced in Los Angeles and all the 2000 units of Drug 1 will be produced in Los Angeles.
Time Required = 333.33 * 0.33 + 2000 * 0.24 = 590, So it has enough capacity to produce both.
Total Cost = 2666.67 * 4.70 + 333.33 * 5.20 + 2000 * 4 = 22266.67
Obviously, both medications are less expensive to make in Indianapolis, thus the company would not choose to purchase an additional hour in Los Angeles.
Hours Required to produce rest of 333.33 units of drug 2 at Indianapolis = 100 hours.
Hours Required to produce all the 2000 units of drug 1 at Indianapolis = 2000 * 0.2 = 400 hours.
So it will purchase 500 hours at Indianapolis.
It would be ready to pay the cost which it will save by making the production at Indianapolis.
Savings in drug 2 = (110-100) * 5.2 + 100 * 0.50 = 102*
Savings in drug 1 = (480 – 400) * 4 + 400 * 0.20 = 400**
Total Savings = 502
Savings per hour = 502/500 = 1.004 or 1
Hours required to produce 333.33 units of drug 2 in Indianapolis is 100 and in Los Angeles is 110. So 10 hours of extra cost of 5.2*10 and 100 hours of extra cost of 0.5*100.
**Hours required to produce 2000 units of drug 1 in Indianapolis is 400 and in Los Angeles is 480. So 80 hours of extra cost of 4*80 and 400 hours of extra cost of 0.2*400.