Question

Please show workings.

To start a transport company, a business man needs at least 5 buses and 10 minibuses .
He is not able to run more than 30 vehicles all together.
A bus takes up 3 units of parking space, a minibus takes up 1 uni of parking space and there are only 54 units available.
If x and y are the number of buses and minibuses respectively.

a. Write down for inequalities which represents the restrictions of the businessman.
b. Draw a gaph that shows a region representing possible values of x and y.
c. Find the greatest number of:
i. buses
ii. minibuses that the business can run​

Answer 1

9514 1404 393

Answer:

a) x≥5; y≥10; x+y≤30; 3x+y≤54

b) see attached

c) i. 14 buses; ii. 25 minibuses

Explanation:

a. The given restrictions are ...

x ≥ 5 . . . . . . . . . minimum number of buses

y ≥ 10 . . . . . . . . minimum number of minibuses

x + y ≤ 30 . . . . .maximum number of vehicles

3x +y ≤ 54 . . . . maximum number of parking units

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b. In the attached, we have chosen to make the solution space white. The boundaries are dashed where they are included in the solution space. The vertices of the solution space are marked on the graph.

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c. The second attachment shows the maximum numbers of each.

i. maximum buses: 14 (and 12 minibuses)

ii. maximum minibuses: 25 (and 5 buses)