Formulate but do not solve the following exercise as a linear programming problem.
Kane Manufacturing has a division that produces two models of fireplace grates, model A and model B. To produce each model A grate requires 4 lb of cast iron and 5 min of labor. To produce each model B grate requires 5 lb of cast iron and 4 min of labor. The profit for each model A grate is $4.00, and the profit for each model B grate is $1.50. If 1,000 lb of cast iron and 25 hr of labor are available for the production of grates per day, how many grates of each model should the division produce per day in order to maximize Kane's profits?
Because of a backlog of orders on model A grates, the manager of Kane Manufacturing has decided to produce at least 150 of these models a day. Operating under this additional constraint, how many grates of each model should Kane produce to maximize profit?
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Solve the problem.You are planning to close off a corner of the first quadrant with a line segment 15 units long running from (x, 0) to (0, y). Show that the area of the triangle enclosed by the segment is largest when 
What will be an ideal response?
Find the volume of the solid. Use 
for ?.
A. 71
cu in.
B. 13
cu in.
C. 2
cu in.
D. 23
cu in.
Factor completely. If the polynomial cannot be factored, write "prime."3x3 + 6x2y - 45xy2
A. 3x(x - 3y)(x + 5y) B. (3x2 + 9xy)(x - 5y) C. 3x(x + 3y)(x - 5y) D. (x - 3y)(3x2 + 15xy)
Find all the second order partial derivatives of the given function.f(x, y) = xy2 + yex2 + 5
A. 
= yex2(1 + 2x2); 
= x; 
= 
= y + xex2
B. 
= 2yex2(1 + 2x2); 
= 2x; 
= 
= 2y + 2xex2
C. 
= 2yex2; 
= 2x; 
= 
= 2y + 2xex2
D. 
= 2yex2; 
= 2x; 
= 
= 2xex2