The gross income of ginger hughes is $212 per week. her deductions are: $15.16,fica tax; $29.33,income tax; 2% state tax; 1%city tak; and 3% retirement fund. what is her net income?

200 software program and 225 video games should be produced per week in order to maximize the profit

Step-by-step explanation:

Let us use the linear program to solve the problem

Assume that x represents the numbers of the software programs and y represents the numbers of the video games per week

∵ The company can produce at most 200 software programs

- At most means ≤

∴ x ≤ 200 ⇒ (1)

∵ The company can produce at most 300 video games

∴ y ≤ 300 ⇒ (2)

∵ The total production cannot exceed 425 items

- Can not exceed means ≤

∴ x + y ≤ 425 ⇒ (3)

Let us draw the graph of the three inequalities

Look to the attached graph

The red part represents x ≤ 200 ⇒ The shaded part is below the line x = 200

The blue part represents y ≤ 300 ⇒ The shaded pert is below the line y = 300

The green part represents x + y ≤ 425 ⇒ The shaded part is below the line x + y = 425

The common solution of the three inequalities is the polygon which contain the three colors together and its vertices are (0 , 0) , (200 , 0) , (200 , 225) , (125 , 300) , (0 , 300)

We will use this vertices to find the maximum profit

∵ The company makes a profit of $50 per software program

   and $35 per video game

- Multiply x by 50 and y by 35, then add the products to get

   the profit

∴ The profit = 50 x + 35 y

Substitute the coordinates of each vertex in the equation to find the maximum profit

At (200 , 0)

∵ x = 200 and y = 0

∴ The profit = 50(200) + 35(0)

∴ The profit = 10000 + 0

∴ The profit is $10,000

At (200 , 225)

∵ x = 200 and y = 225

∴ The profit = 50(200) + 35(225)

∴ The profit = 10000 + 7875

∴ The profit is $17,875

At (125 , 300)

∵ x = 125 and y = 300

∴ The profit = 50(125) + 35(300)

∴ The profit = 6250 + 10500

∴ The profit is $16,750

At (0 , 300)

∵ x = 0 and y = 300

∴ The profit = 50(0) + 35(300)

∴ The profit = 0 + 10500

∴ The profit is $10,500

The maximum profit is $17,875 with x = 200 and y = 225

200 software program and 225 video games should be produced per week in order to maximize the profit