2) an engineer is trying to formulate the minimum cost set of materials to use in an upcoming project. there are four groups of materials, and exactly one item from each group must be selected. the costs are given below: group a cost group b cost group c cost group d cost a1 10 b1 2 c1 8 d1 5 a2 12 b2 1 c2 9 d2 8 a3 16 c3 11 d3 9 c4 13 if b2 is selected, then a3 must be used. we can use at most one of a1, b1, c1, and d1, while we must have at least two of a3, c3, c4, and d3. finally, d1 cannot be used unless a2 or c4 is used. formulate and solve a 0-1 integer programming model that will determine the optimal solution.

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

d. all of the above

step-by-step explanation:

b

step-by-step explanation: