Provide an appropriate response.To fill an order for 100 units of a product, a firm wishes to distribute the production between its two plants, Plant 1 and Plant 2. The total cost function is given byc = f(q1, q2) = 0.5
+ 2q1 + 32q2 + 500, where q1 and q2 are the number of units produced at Plants 1 and 2, respectively. How should the output be distributed in order to minimize costs?
What will be an ideal response?
q1 = 30, q2 = 70
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Find the domain and graph the function.F(x) = 
A. D: (-?, 0)
B. D: (-?, ?)
C. D: [0, ?)
D. D: (-?, 0]
Solve the inequality algebraically.-3.8x + 8.1 > 16.08
A. x < 2.1 B. x < -2.1 C. x > 2.1 D. x > -2.1
Find all the second order partial derivatives of the given function.f(x, y) = cos (xy2)
A. 
= - y2 sin xy2; 
= 2y
; 
= 
= 2
B. 
= -y4 cos xy2; 
= - 2x[2xy2 cos (xy2) + sin(xy2)]; 
= 
=
- 2y[xy2 cos (xy2) + sin(xy2)];
C. 
= y2 sin xy2; 
= 2[2y2 cos (xy2) - sin (xy2)] ; 
= 
= 2y[y2 cos (xy2) - sin (xy2)]
D. 
= - y2 sin xy2; 
= 2[ sin (xy2)- 2y2 cos (xy2)] ; 
= 
= 2y [sin (xy2)-y2 cos (xy2)]
Solve the problem. Round your answer, if appropriate.The volume of a sphere is increasing at a rate of 6 cm3/sec. Find the rate of change of its surface area when its volume is 
cm3. (Do not round your answer.)
A. 12? cm2/sec
B. 
cm2/sec
C. 8 cm2/sec
D. 12 cm2/sec