Question

A company makes a profit of $75 per software program and $125 per video game. The company can produce at most 350 software programs and at most 200 video games per week. Total production cannot exceed 475 items per week. How many items of each kind should be produced per week in order to maximize the profit? Use liner programming to solve. Let x = software programs
Let y = video games

Answer 1

The company should produce 275 units of software programs, and 200 units of video games to get a maximum profit of $45625

A profit of $75 per software program and $125 per video game means that, the objective function is:

$Max\ P = 75x + 125y$

The company's weekly production means that, the constraints are:

$x \le 350$ --- at most 350 software programs

$y \le 200$ --- at most 200 video games

$x + y \le 475$ --- the total production cannot exceed 475

So, the linear model is:

$Max\ P = 75x + 125y$

Subject to

$x \le 350$

$y \le 200$

$x + y \le 475$

$x,y\ge 0$

See attachment for the graphs of the constraints

From the graph, we have the following ordered pairs

$(x,y) = \{(275,200)\ (350,125)\}$

Substitute these values in the objective function

$Max\ P = 75x + 125y$

(275,200)

$P = 75 \times 275 + 125 \times200$

$P = 45625$

(350,125)

$P = 75 \times 350 + 125 \times 125$

$P = 41875$

By comparison; 45625 > 41875

Hence, the company should produce 275 units of software programs, and 200 units of video games to get a maximum profit of $45625

Read more about linear programming at:

https://brainly.com/question/15356519