3. a company makes a profit of $20 per software program and $8 per video game. the company can produce at most 100 software programs and at most 150 video games per week. total production cannot exceed 225 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:

step-by-step explanation:

you don't need linear programming to solve this problem. simple logic tells you that profit will be maximized when the company produces as many as it can of the highest-profit item (software programs), and fills in the rest of the production capacity with the next-highest profit item.

at most, 100 software programs can be produced, so that number should be. the remaining capacity of 225-100 = 125 items is less than the possible number of video games that can be produced, so that capacity should be used by producing video games.

if you were to solve this graphically, the point on the boundary of the feasible region that puts the profit curve farthest from the origin is (x=programs, y=games) = (100, 125).

comment on solution by linear programming

the simplex method of solution of this problem would find the pivot by looking at the profit per item and choosing the item that has the maximum profit. it would allocate production capacity to that item up to the limit of production capacity for that item. the logic is exactly the same as described above, only it is expressed in terms of choosing rows and columns and computing numbers in a table.

I think the ordered pair is (1,10)