clever 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. develop a linear programming model to minimize production costs and determine how many of each type of ball should be produced to meet the required demand.