The JFA company has developed two new gadgets for possible inclusion in the product line for the upcoming Halloween. Setting up for production for gadgets A and B would cost $5,000 and $7,000, respectively; and profit per unit is expected to be $3 and $6 for gadgets A and B, respectively. Although the JFA has two plants, it is decided that only one plant will be utilized for production of the gadgets. Plant 1 can produce gadget A at a rate of 25 units/hour and gadget B at a rate of 35 units/hour. Plant 2 can produce gadget A at a rate of 45 units/hour and gadget B at a rate of 22 units/hour. Available capacity at the Plants 1 and 2 until Halloween are 800 and 750 hours, respectively. The problem is to determine how many (if any) units of each gadget to produce before Halloween in order to maximize profit. Formulate this problem as a mixed integer program