Item$2$

$10$

points

Item $2$

a$.$ An appliance manufacturer produces two models of microwave ovens: H and W$.$ Both models require fabrication and assembly work; each H uses four hours of fabrication and two hours of assembly, and each W uses two hours of fabrication and six hours of assembly. There are $600$ fabrication hours available this week and $480$ hours of assembly. Each H contributes $$40$ to profits, and each W contributes $$30$ to profits. What quantities of H and W will maximize profit?

Use either the objective function or enumeration method.

b$.$ The company also produces two refrigerator models: large $($L$)$ and medium $($M$).$ Although materials to produce the refrigerators is available, fabrication time and assembly time are limited$.$ There are $540$ hours available for fabrication and $600$ hours available for assembly this week. Each unit of model L requires $6$ hours for fabrication and $3$ hours for assembly, and each unit of M requires $4$ hours for fabrication and $5$ hours for assembly. Each unit of L contributes $$50$ to profit, and each unit of model M contributes $$40$ to profit. How many units of each model should be produced if the objective is to maximize profit? $($Round $"$L$"$ to $2$ decimal places.$)$

Use either the objective function or enumeration method.