How much candy at $1.20 a pound should be mixed with candy worth 95¢ a pound in order to obtain a mixture of 50 pounds of candy worth a dollar a pound?

10 pounds of candy costing $1.20 per pounds must be mixed with 40 pounds of candy costing $ 0.95 per pound to obtain a 50 pounds of candy costing $ 1 per pound

Solution:

Let "x" be the pounds of candy at $ 1.20 per pound

Then (50 - x) is the pounds of candy at $ 0.95 per pound ( since 95 cents is equal to 0.95 pound)

Therefore, x pounds of candy costing $1.20 per pounds must be mixed with (50 - x)  pounds of candy costing $ 0.95 per pound to obtain a 50 pounds of candy costing $ 1 per pound

Then the equation becomes,

1.20x + (50 - x)0.95 = 50 x 1

On expanding we get,

1.20x + 47.5 - 0.95x = 50

0.25x = 50 - 47.5

0.25x = 2.5

x = 10

Then (50 - x) = 50 - 10 = 40

So we need 10 pounds of candy worth $ 1.20 per pound and 40 pounds of candy worth $ 0.95 to obtain 50 pounds of candy worth a dollar a pound

answer: evaluate the objective function at each vertex to determine which - and -values, if any, maximize or minimize the function. example: find the minimum value and maximum value of the objective function f ( x , y ) = 4 x + 5 y , subject to the following constraints