word problem

Question

It costs a bakery $3 to make a cake and $4 to make a pie. Production costs cannot exceed $120 per day. Write the system of inequalities that represents this situation and graph its solution region. 

How do I write this inequality?

Answer 1

c = number of cakes

p = number of pies

 

c ≥ 0
p ≥ 0
because we will never make a negative number of cakes or pies.

This means your final shaded area will all be within quadrant I where
both variables are positive or zero.

 

Your equation for the inequality based on production cost is:

3c + 4p ≤ 120

 

Take the line  3c + 4p = 120 and graph points

 

c       |      p

-------------

0       |    30

40     |      0

 

 

draw the line on the Cartesian coordinate system.

I have the "x axis" as number of cakes and the

"y axis" as number of pies.  The line will be solid,

not dashed because the total can be equal to $120

 

This way the slope is negative because the more

cakes you make, the less the number of pies made.

 

Pick a point under the line such as (0,0)

Plug this into your inequality

 

3(0) + 4(0) ≤ 120

0 ≤ 120

 

Since this is a true statement then the area below

your line is the area shaded... but only the area

to the right of the "y" or p-axis and above the

"x" or c-axis as stated earlier.