Linear Programming
Name Turbo
.
1.) Jack has 2800 acres of farmland. He needs to determine how much of two different types of crops to plant. Crop A
brings in $240 per acre, while crop B brings in $270 per acre. Some regulations say that he can plant no more than 2000
acres of crop A and no more than 1200 of crop B. Find the proper balance of crop A and crop B that satisfies the
conditions and gives the maximum income. What is the maximum income?
240 A  270 B  C
240(1600)  270(1200)  708000
240(2000)  270(800)  696000
So For Maximum income Jack should plant 1600 acres of crop A and 1200 acres of Crop B for an income of $708,000.
2.) A. manufacturer can show a profit on a bicycle of $6 and a profit on a tricycle of $4. Department A requires 3 hours to
manufacture the parts for a bicycle and 4 hours to manufacture the parts for a tricycle. Department B takes 5 hours to
assemble a bicycle and 2 hours to assemble a tricycle. How many bicycles and tricycles should be produced to maximize
the profit if the total time available in department A is 450 hours and in department B is 400 hours? What is the maximum
profit?
6x  4 y  C
6(0)  4(112.5)  450
6(50)  4(75)  600
6(80)  4(0)  480
So the maximum profit of $600 occurs when we manufacture 50 bicycles and 75 tricycles.
3.) A pharmaceutical company manufactures two drugs. Each case of drug one requires 3 hours of processing time and 1
hour of curing time per week. Each case of drug two requires 5 hours of processing time and 5 hours of curing time per
week. The schedule allows 55 hours of processing time and 45 hours of curing time weekly. The company must produce
no more than 10 cases of drug one and no more than 9 cases of drug two. If the company makes a profit of $320 on each
case of drug one and $500 on each case of drug two, how many cases of each drug should be produced in order to
maximize profit?
320 A  500 B  C
320(5)  500(8)  5600
320(10)  500(5)  5700
The maximum profit of $5700 occurs when we manufacture 10 cases of drug 1 and 5 cases of drug 2.
4. A company is planning to buy new fork hoists for material handling. There are two models that will serve their needs.
The supplier has 8 Model M hoists and 10 Model R hoists on hand for delivery. The company purchasing agent has
decided that no more than 14 hoists can be purchased. Model M can handle 12,000 kg per hour and Model R can handle
10,000 kg per hour. What number of hoists of each model should be purchased for maximum weight handling capacity?
What is the maximum handling capacity?
12000 M  10000 R  C
12000(4)  10000(10)  104800
12000(8)  10000(6)  69600
So if we buy 4 Models M and 10 Models R we will maximize our lift capacity at 104,800 tons per hour.