Question

A toy manufacturer makes a toy truck, a toy car, and a toy boat. The production spreadsheet is:

Toy - Time to Produce - Cost to Produce - Profit for Each
Truck - 10 minutes - $1.00 - $1.00
Car - 12 minutes - $0.75 - $1.50
Boat - 8 minutes - $0.80 - $0.60
After accounting for breaks, a worker actually works 400 minutes each day. The manufacturer needs each worker to generate a potential profit of $35 each day.
Write a system of inequalities that expresses these constraints.

Answer 1

Time:

Car > Truck > Boat.

Cost of produce:

Truck > Boat > Car

Profit

Car > Truck > Boat.

We know that a worker works 400 minutes each day, and the profit that each worker needs to generate is $35, let's find how each worker needs to spend their time.

Let's call T to the number of trucks he makes, C for cars and B for boats.

Then, if he works 400 minutes we have:

T*10 + C*12 + B*8 ≤ 400

this means that the time expended crafting the toys can be, at most, 400 minutes (here you use the inequality because the worker actually can be less effective than the max, maybe tacking a break or something like that)

The other equation is:

T*1 + C*1.5 + B*0.6 ≥ 35

Here we use the inequality because the profit needs to be at least 35$, none the less, the profit can be more than tath.

Notice that if we want to solve the system with for the equal signs, it is:

T*1 + C*1.5 + B*0.6 = 35

T*10 + C*12 + B*8 = 400

We have 3 variables and 2 equations, this means that there are more than one solution for this system.