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. for the next month, the total production hours of 500 are available. also, it is given that the combined production quantity for these two balls must be at least 150 units. the objective for this linear programming model is to fulfil the given production requirements at a minimum cost for the total production. the production cost for each soccer ball is $9 and each cork ball is $7. formulate and solve an all-integer model that will determine the recommended production quantities.