Question

3. A company makes a profit of $15 per software program and $10 per video game. The company can produce

at most 70 software programs and at most 80 video games per week. Total production cannot exceed 100

items per week. How many items of each kind should be produced per week in order to maximize the profit?

Use linear programming to solve. Show all your work.

Answer 1

Answer:

For the profit to be maximized, 20 software programs and 80 video games should be produced

Step-by-step explanation:

Let x represent the number of the software programs and let y represent the number of video games.

We are told that the company can produce at most 70 software programs and then, at most 80 video games per week. Thus;

x ≤ 70

y ≤ 80

Also, we are told that the overall production cannot exceed 100. Thus;

x + y ≤ 100

Since the company makes a profit of $15 per software program and $10 per video game. Then, the function to be maximized is;

15x + 10y

When they produce at most 70 software programs, it means that the number of video games that can be produced is: 100 - 70 = 30.

Thus, one point of maximizing values is; (70, 30)

Also, when they produce at most 80 video games per week, the number of software programs that can be produced is; 100 - 80 = 20.

Thus, second point of maximization is;

(20, 80)

Putting these points into the objective function, we have;

At (70, 30); 15(70) + 10(30) = $1350

At (20, 80); 15(20) + 10(80) = $1100

For the profit to be maximized, 20 software programs and 80 video games should be produced