A Haberdashery Produces Scarves, Ascots, and Capes

Essay

A haberdashery produces scarves, ascots, and capes.The profit function for the haberdashery is expressed by the following equation: profit = 4S + 2A + 5C + 0.8S² + 1.4A² + 2C² + 2SAC.It takes 9 minutes to produce a scarf, 13 minutes to produce an ascot and 30 minutes to produce a cape.There is also a nonlinear element to the usage of time governed by the double the product of scarves, ascots and capes produced.There is a total of 50 hours available for labor each week.Shipping poses another issue for the haberdashery; packaging and loading trucks for online orders is time consuming and that function is handled by the haberdashery owner's mother who comes in after her afternoon walk around a local almost-deserted mall.It takes 1.5 minutes to pack and load a scarf, 2.5 minutes to pack and load an ascot, and 3.5 minutes to pack and load a cape.There is also a cross product term for packing and loading that is 0.15SA + 0.075SC + 0.025AC that must be considered.The haberdasher's mother is available only 30 hours a week, but the haberdasher is prepared to lay down the law and insist she stop this mall walking foolishness and devote herself completely to his business.For the time being, consider her time as only 30 hours.There must be at least 50 scarves, 100 ascots, and 25 capes produced each week.Formulate a nonlinear integer program representing the profit maximization problem for the haberdashery.