"the munchies cereal company makes a cereal from several ingredients. two of the ingredients, oats and rice, provide vitamins a and b. the company wants to know how many ounces of oats and rice it should include in each box of cereal to meet the minimum requirements of 48 milligrams of vitamin a and 12 milligrams of vitamin b while minimizing cost. an ounce of oats contributes 8 milligrams of vitamin a and 1 milligram of vitamin b, whereas an ounce of rice contributes 6 milligrams of a and 2 milligrams of b. an ounce of oats costs $0.05, and an ounce of rice costs $0.03. a. formulate a linear programming model for this problem. b. solve this model by using graphical analysis."

8x + 6y >/= 48 ......1

x + 2y >/= 12 .......2

The cost function is given as;

C = 0.05x + 0.03y .........3

The minimum cost is $0.24 at (0,8)

That is 0 ounces of oats and 8 ounces of rice.

Step-by-step explanation:

let x represent the number of ounces of oats

And y represent the number of ounces of rice

For Vitamin A

Minimum requirements = 48mg

x ounces of oats contribute 8mg × x

y ounces of Rice contribute 6mg × y

Therefore, we have;

8x + 6y >/= 48 ......1

For Vitamin B

Minimum requirements = 12mg

x ounces of oats contribute 1mg × x

y ounces of Rice contribute 2mg × y

Therefore, we have;

x + 2y >/= 12 .......2

The cost function is given as;

C = 0.05x + 0.03y .........3

Attached is the graphical representation.

The feasible points are (x,y) = (0,8),(2.4,4.8),(12,0)

The minimum cost is determined by substituting each point into the cost function

For (0,8)

C= 0.05(0) + 0.03(8)

C = $0.24

For (12,0)

C= 0.60

For (2.4,4.8)

C= $0.264

The minimum cost is $0.24 at (0,8)

25 questions , because they start with 100.  

350-100=250 .  

. 250/10=25

step-by-step explanation:

first take off 100, then what x 10 = 250? that is your answer. (25)

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).