Question

1. Orange, Inc. produces two models of oPhones. Model A sells for $700 and model B sells for $500. The cost to produce model A is $500 and the cost to produce model B is $325. Orange expects to sell at least 90 units of model A and 100 units of model B per day. Orange can produce no more than 300 units per day, regardless of model. How many of each model should Orange produce to maximize profit and what will the maximum profit be?

Answer 1

a) Choose a variable for each product.
Let a be the number of units of model A and b be the number of units of model B.

b) Form a total profit statement.
Model A sells for $700 and costs $500 to produce. Therefore
P = 700 – 500
P = 200

Model B sells for $500 and costs $325 to produce. Therefore
P = 500 – 325
P = 175

So the total profit is
P (a,b) = $200a + $ 175b

c) Write your constraints as a system of inequalities.
The fewest units that can be produced is 0. Therefore,
a ≥ and b ≥

The maximum units that can be produced is 300, so
a + b

Based upon customer demand,
a ≥ and b ≥

d) Graph the system.
Let’s start with the constraints on units. These two limit us to the first quadrant.

Now let’s graph customer demand using the green arrows below. These are the inequalities in the third part from step c. Drag the arrows onto the graph, stretching and rotating them as needed.

Now graph the maximum number of units that can be sold using the purple arrow below. This is the inequality for a + b that you found in the second part from step c. Drag the arrows onto the graph, stretching and rotating them as needed.

Look at the polygon formed. You should see a triangle.

e) List the vertices of the polygon formed.
They are ( , ), ( , ), and ( , ).

f) Evaluate the vertices in the profit statement and choose the most viable option. Show all your work below and complete the statement below.

The most profitable solution is the one that yields the highest value for P. Orange should produce units of model A and units of model B, which will yield $ in profit.