I NEED ALL WORK SHOWN. PLEASE SHOW ALL WORK - I DONT UNDERSTAND THIS PROBLEM PLE

Question

I NEED ALL WORK SHOWN. PLEASE SHOW ALL WORK - I DONT UNDERSTAND THIS PROBLEM

PLEASE DONT GIVE ME VALUES AND ASSUME I CAN SOLVE IT ON MY OWN

A craftsman makes two kinds of jewelry boxes for craft shows. The oval box requires 30 minutes of machine work, and 20 minutes of finishing. The square box requires 20 minutes of machine work and 40 minutes of finishing. Machine work is limited to 600 minutes per day and finishing 800 minutes. There is $3 profit on the oval box and $4 profit on the square box, how many of each should be produced to maximize profit?

a) define all variables, set up a linear programming problem that describes the question

b) using graph paper, plot the constraint set, SHADE THE APPROPRIATE FEASIVLE REGION

c) determine all corner points for the feasible region, using the objective function evaluate it as each corner point and determine which point gives the maximum.

Explanation / Answer

First we need to set up vairableslet x = number of oval boxeslet y = number of square boxesHere are the constraints:30x+20y=0Now we can find out the vertices of the graphNow we can find out which region is shadedThe first intersection pt is done by setting the first two equations equal to eachother-30x/20+600/20 = -20x/40+800/40-3x/2 + 30 =-x/2+20x= 10y=-3(10)/2+30 = 15(10,15)The other intersection points is the y-intercept for the second eqn and x interce

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