Goldilocks needs to find at least 12 lb of gold and at least 18 lb of silver to pay the monthly rent. there are two mines in which goldilocks can find gold and silver. each day that goldilocks spends in mine 1, she finds 2 lb of gold and 2 lb of silver. each day that goldilocks spends in mine 2, she finds 1 lb of gold and 3 lb of silver. formulate an lp to goldilocks meet her requirements while spending as little time as possible in the mines. graphically solve the lp.

To minimize the time spent to achieve the goal, Goldilocks

must spend 4 days and a half in mine 1 and 3 days in mine 2

Step-by-step explanation:

Let's call x the number of days Goldilocks spends on mine 1 and y the number of days it spends on mine 2 to meet the requirements.

Then  

2x + y is the amount of gold found in both mines and

2x + 3y  is the amount of silver found in both mines

We have the constraints  

a) 2x + y≥ 12

b) 2x + 3y ≥ 18

and we want to minimize the total time spent to accomplish this goal. That is, we want to find x and y such that

x+y is minimum.

We then draw in the xy-plane the regions a) and b) and find the feasible region which is the intersection of both regions

The line 2x + y =12 (GREEN) has x-intersect x=6 and y-intersect y=12

The line 2x + 3y =18 (BLUE) has x-intersect x=9 and y-intersect y=6

The point P is the intersection (x,y) of the two lines, that is, the result of solving the linear system

2x + y = 12

2x + 3y = 18

The solution of this system can easily be found and gives us

P=(4.5, 3)

As the function z = x + y is linear, its minimum is attained in one of the vertices (0,12), (9,0) or (4.5,3).

A direct evaluation of z in each one this points, gives as a result that the minimum is reached in (4.5,3)

So, to minimize the time spent to achieve the goal, Goldilocks

must spend 4 days and a half in mine 1 and 3 days in mine 2.

i think it would be 43 movies that would have to be watched.

step-by-step explanation:

think about it. for the second plan, every month is 8 dollars. 8 x 12= 96. so thats the number for the second plan. now for the first plan, its annual meaning you have to pay 10 dollars every year. so now you have to get an equivalent amount of 86 since 96-10=86. 86 divided by 2 since every movie costs 2$ then you would have to watch 43 movies a year to get the same as the second plan. i really hoped this . have a wonderful day as well!