a company makes a profit of $50 per software program and $35 per video game. The company can produce at most 200 software progra

Question

3 months ago

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a company makes a profit of $50 per software program and $35 per video game. The company can produce at most 200 software progra

ms and at most 300 video games per week. Total production cannot exceed 435 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.

Mathematics

2 answers:

Svet_ta [12.7K] · Answer 1 · 2026-02-20T22:20:18+03:00

Answer:

To achieve maximum profit, the weekly production should be 200 software programs and 235 video games.

Step-by-step explanation:

Let:

x ------> represent the number of software programs

y -----> denote the count of video games

We are aware that

$x \leq 200$ ------> inequality A

$y \leq 300$ ------> inequality B

$x+y \leq 435$ ------> inequality C

Utilizing a graphing method

The feasible solutions exist in the area marked between the positive values of x and y

Refer to the attached diagram

The vertices of this area are:

(0,0),(0,300),(135,300),(200,235),(200,0)

The profit function computes as:

$P=50x+35y$

Plugging the x and y values from each vertex into the profit function, we get:

For (0,300) ----- $P=50(0)+35(300)=\$10,500$

For (135,300) ----- $P=50(135)+35(300)=\$17,250$

For (200,235) ----- $P=50(200)+35(235)=\$18,225$

For (200,0) ----- $P=50(200)+35(0)=\$10,000$

Consequently,

To optimize the profit, the weekly production should consist of 200 software programs and 235 video games.

babunello [11.8K] · Answer 2 · 2026-02-20T22:19:37+03:00

babunello [11.8K]3 months ago

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