1. Linear programming

2. Linear Programming Question #1
The owner of a store wishes to buy x radios and y televisions to sell to the public. The total number of sets must however not exceed 20.
He buys each radio at a cost of $150 and each television at a cost of $300, but he spends no more than $4500 on the sets. He also buys at least 5 of each set.
(i) Write down 4 inequalities which satisfy the given information
(ii) Graph the system of inequalities and shade the solution set.
(iii) If when the store owner sells the sets he makes a profit and the number of each set he must sell to obtain the maximum profit.

3. Linear Programming x radios y televisions x + y ≤ 20 x ≥ 5 y ≥ 5

4. Y - television
x ≥ 5 20 15 5
X -radio 5 20 30

5. Y - television
x + y ≤ 20 20 15 5
X -radio 5 20 30

6. Y - television 20 15
y ≥ 5 5
X -radio 5 20 30

7. Y - television 20 15 5
x + 2y ≤ 30
X -radio 5 20 30

8. x + 2y = 30 Y - television X ≥ 5 x + y ≤ 20 20 15 y ≥ 5 5 5 20 305 20 30
X -radio

9. Linear Programming Question #2
A parking lot allows parking for x trucks and y cars. The total number of vehicles in the lot must not exceed 30. The number of cars must be at least equal to the number of trucks in the parking lot. At any instant, there must be at least 5 trucks and not more than 20 cars in the parking lot.

10. Linear Programming Question #2
(i) Write 4 inequalities which satisfy the given information.
(ii) Graph the system of inequalities and shade the solution set.
(iii) If the charges are $5 for a car and $8 for a truck, determine how many of each kind should be admitted to the parking lot to maximize income.

11. Linear Programming
x trucks y cars
The number of cars must be at least equal to the number of trucks
y ≥ x

12. Linear Programming
x trucks y cars
x + y ≤ 30
y ≥ x
x ≥ 5
y ≤ 20

13. Y - cars
x + y ≤ 30 30 15 5
X -trucks 5 20 30

14. Y - cars
y ≥ x 30 15 5
X -trucks 5 20 30

15. Y - cars
X ≥ 5 30 15 5
X -trucks 5 20 30

16. Y - cars 30
y ≤ 20 20 15 5
X -trucks 5 20 30

17. Y - cars
x ≥ 5
x + y ≤ 30
y ≥ x 30
y ≤ 20 15 5
X -trucks 5 20 30

18. Home Work (Have fun!)
A farmer wishes to graze X cows and Y sheep. He has pastures for only 120 animals. He decides that the number of sheep must not be more than twice the number of cows and that there must be at least 30 cows and at least 50 sheep.
(i) Write down 4 inequalities which satisfy the given information
(ii) Graph the system of inequalities and shade the solution set.
(iii) The farmer makes a profit of $250 on each cow and $100 on each sheep he sells.
How many of each type of animal must he graze and sell to earn maximum profit.