a yard produces two special wines, a white and a red. a bottle of the white wine requires 14 pounds of grapes and 1 hour of processing time. a bottle of red wine requires 25 pounds of grapes and 2 hours of processing time. the vineyard has on hand 2,198 pounds of grapes and can allot 160 hours of processing time to the production of these wines. a bottle of the white wine sells for $11.00 while a bottle of the red wine sells for $20.00. how many bottles of each type should the vineyard produce in order to maximize gross sales?

Question

anonymous · Answer

help

anonymous · Answer

Let w represent white wine and r represent red wine
we need to equations to solve for these two variable, one will be an equation of total hours and the other of total pounds of grapes
Total hours=160 so
1*w+2*r=160
Total weight=2198 so
14*w+25*r=2198

now solve for one variable in one equation and substitute that expression into the other equation to solve for both variables

anonymous · Answer

still lost

anonymous · Answer

so
w=160-2r
now plug that expression for w into the other equation and you can solve for the number of bottle of red wine

anonymous · Answer

if you let me know exactly what your stuck on i can try to help with it

anonymous · Answer

what i plug into i understand the equations but dont know what i plug in

anonymous · Answer

so w=160-2r and
14*w+25*r=2198 which is equal to
14*(160-2r)+25*r=2198 
because we solved the other equation in terms of w we can plug that into the second equation
now that equation is reduced to only one variable which we can solve for

anonymous · Answer

once we know the value for r we can plug it into one of the equations and solve for w