Sporting Equipment, Inc. makes two types of balls: Soccer balls and Cork balls. The making of each soccer ball and cork ball requires 3 hours and 4 hours of production time, respectively. A total of 500 production hours are available during the next month At least 150 balls, combined, must be produced. The production cost for each Soccer ball is $9 and each Cork ball is $7.Formulate and solve a linear programming model minimizing production costs.

100 soccer balls and 50 cork balls must be produced

Step-by-step explanation:

Let the number of soccer ball = p  and number of cork ball = q

Production hours of p = 3 hours

Production hours of q = 4 hours

Then the production time equation would be:

3p + 4q ≤500

The number of the balls must be at least 150

p + q ≥150

x ≥ 0     y ≥ 0

Minimum production r = 9p + 7q

Therefore 100 soccer balls and 50 cork balls must be produced

< coa = 150 ( given)

as ba and bc are tangents

so oc and oa is perpendicular to cb and ab respectively because in circle normal passes through centre

so in quadrilateral oabc

< coa + < oab + < ocb + < abc = 360

150 +90+90 + < abc = 360

330 + < abc = 360

< abc = 360 -330 = 30

so < abc = 30

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