"A manufacturing company produces widgets using two different machines, Machine A and Machine B$.$ Machine A produces widgets at a rate of $100$ units per hour with a defect rate of $5\%,$ while Machine B produces widgets at a rate of $120$ units per hour with a defect rate of $8\%.$ If the company needs to produce $1000$ defect$-$free widgets in the shortest time possible, how should they allocate production between the two machines to minimize production time and costs?"