Question

A new electronics company, HOTWIRED, is working on two new docking stations to release this

summer for their new phone they are releasing. The company has compiled the constraints and
limitations on creating these new docking stations. Given the graph, x denotes the number of
basic models and y is the number of advanced models. The accounting department says that
they will make $55 on each basic model and $95 on each advanced model. How many of each
model should they sell to make the
maximum profit?

Answer 1

The objective function is P(x,y) = 55x + 95y

P(600, 1400) is $166000

P(600, 1700) is $194500

P(1500, 1700) is $244000

P(1200, 800) is $142000

P(1500, 800) is $158500

They need to sell 1500 of the basic models and 1700 of the advanced models to make the maximum profit

Explanation:

Let us solve the question

∵ x denotes the number of basic models

∵ y is the number of advanced models

∵ They will make $55 on each basic model

∵ They will make $95 on each advanced model

→ The profit is the total amount of money-making on them

∴ Profit = 55(x) + 95(y)

∴ Profit = 55x + 95y

∴ The objective function is P(x,y) = 55x + 95y

Let us test the vertices on the objective function

∵ The vertices are (600, 1400), (600, 1700), (1500, 1700), (1200, 800),

and (1500, 800)

→ substitute each vertex in the objective function

∵ x = 600 and y = 1400

∴ P(600, 1400) = 55(600) + 95(1400) = 166000

∴ P(600, 1400) = $166000

∵ x = 600 and y = 1700

∴ P(600, 1700) = 55(600) + 95(1700) = 194500

∴ P(600, 1700) = $194500

∵ x = 1500 and y = 1700

∴ P(1500, 1700) = 55(1500) + 95(1700) = 244000

∴ P(1500, 1700) = $244000

∵ x = 1200 and y = 800

∴ P(1200, 800) = 55(1200) + 95(800) = 142000

∴ P(1200, 800) = $142000

∵ x = 1500 and y = 800

∴ P(1500, 800) = 55(1500) + 95(800) = 158500

∴ P(1500, 800) = $158500

∵ The greatest profit is $244000

→ That means the maximum profit will be with vertex (1500, 1700)

∴ They need to sell 1500 of the basic models and 1700 of the

advanced models to make the maximum profit