Z-Salon profits $12 on each manicure and $18 per haircut. A manicure takes 30 minutes and a haircut takes 50 minutes. There are 5 stylists who each work 6 hours per day (that is a total of 360 min x 5 = 1800 minutes in available labor). The salon can schedule 50 appointments per day. How many manicures and how many haircuts should be scheduled each day in order order to maximize profit? What is the maximum profit?
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
13)
Z-Salon profits $12 on each manicure and $18 per haircut. A manicure takes 30 minutes and a haircut takes 50 minutes. There are 5 stylists who each work 6 hours per day (that is a total of 360 min x 5 = 1800 minutes in available labor). The salon can schedule 50 appointments per day. How many manicures and how many haircuts should be scheduled each day in order order to maximize profit? What is the maximum profit?
Let’s get you started.
Let x = number of manicures
Let y = number of haircuts
OBJECTIVE
The objective (goal) is to maximize profit, P. So the objective equation is
P = ______________________________________________ objective equation
CONSTRAINTS:
1)
2)
3)
4)
Now graph the above system of inequalities (constraints) on your graph paper:
Find all vertices (corner points) of your shaded region. Plug them in one at a time into
the objective. Note the one which makes P the biggest. This one is our solution.
Corner Pt (x,y) Objective Value (Profit)
1.
2.
3.
4.
The number of manicures , x = ____
The number of haircuts, y = ____
Maximum Profit, P = ____
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