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This is the fifteenth problem of mathematics in Zhejiang Volume 20 17. How to do this linear programming solution? This is a circle with a radius of 10.
Draw a picture. It is a circle and a rectangle × point (m, n) that falls on the circle and is inside the rectangle.
Let C=m+n, then the straight line n=-m+C takes the maximum value at the tangent point of the first quadrant of the circle.
c/√( 1^2+ 1^2)=√ 10,c=√20=2√5，
When m=3, n= 1, or m= 1, n=3, the minimum value C= 1+3=4 is obtained.