Answer:
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
Step-by-step 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
