Question

In most linear programming problems, there are two stages:

1. to interpret the information given as a series of simultaneous
inequalities and display them graphically.
2. to investigate some characteristic of the points in the unshaded
solution set.
Example
A shopkeeper buys two types of cat food for his shop: Bruno at 40c
a tin and Blaze at 60c a tin. He has $15 available and decides to buy at
least 30 tins altogether. He also decides that at least one third of the
tins should be Blaze. He buys x tins of Bruno and y tins of Blaze.
a) Write down three inequalities which correspond to the above conditions.
b) Illustrate these inequalities on a graph.






Can someone help please (C) is the complete of the question ,the one that is in the photo, I would really appreciate yout anwers༼ つ ◕◡◕ ༽つ

Answer 1

Answer: Bruno = 16 cans, Blaze = 14 cans

Explanation:

Part A gave you the three equations.

Part B showed you the intersected points --> (16, 14), (20, 10), & (21.4, 10.7)

Part C is giving you the Cost function: C(x, y) =0.10x + 0.20y

Input the intersected points into the Cost function to find the maximum.

C(16,14) = 0.10(16) + 0.20(14)

= 1.60 + 2.80

= 4.40

C(20,10) = 0.10(20) + 0.20(10)

= 2.0 + 2.00

= 4.00

C(21.4,10.7) = 0.10(21.4) + 0.20(10.7)

= 2.14 + 2.14

= 4.28

Of the three results we just found, 4.40 is the biggest value.

So, the maximum occurs at C(16,14) = 4.40

↓ ↓

Bruno Blaze