Chapter 5.6, Problem 28PE

(a)

To determine

To calculate: The number of model $A$ units and the number of model $B$ units that should be produced to maximize profit assuming that all furniture will be sold, if a manufacturer produces two models of a patio furniture, Model $A$ requires $2\text{hr}$ for assembly and $1.2\text{hr}$ for painting and Model $B$ requires $3\text{hr}$ for assembly and $1.2\text{hr}$ for painting, the production information and profit for each grill are listed in below table.

	Assembly	Packaging	Profit
Model $A$	$\text{2hr}$	$1.2\text{hr}$	$\$150$
Model $B$	$\text{3hr}$	$\text{1}\text{.5hr}$	$\$200$

The manufacturer has $1200\text{hr}$ of labor available for assembly and $660\text{hr}$ labor available for painting.

(b)

To determine

To calculate: The maximum profit under these constraints, if a manufacturer produces two models of a patio furniture, Model $A$ requires $2\text{hr}$ for assembly and $1.2\text{hr}$ for painting and Model $B$ requires $3\text{hr}$ for assembly and $1.2\text{hr}$ for painting,

The production information and profit for each grill are listed in below table.

	Assembly	Packaging	Profit
Model $A$	$\text{2hr}$	$1.2\text{hr}$	$\$150$
Model $B$	$\text{3hr}$	$\text{1}\text{.5hr}$	$\$200$

The manufacturer has $1200\text{hr}$ of labor available for assembly and $660\text{hr}$ labor available for painting.

(c)

To determine

To calculate: The profit to be maximize if the profit on model $A$ units is $\$180$ and the profit on model $B$ units is unchanged, if a manufacturer produces two models of a patio furniture, Model $A$ requires $2\text{hr}$ for assembly and $1.2\text{hr}$ for painting and Model $B$ requires $3\text{hr}$ for assembly and $1.2\text{hr}$ for painting, the production information and profit for each grill are listed in below table

	Assembly	Packaging	Profit
Model $A$	$\text{2hr}$	$1.2\text{hr}$	$\$150$
Model $B$	$\text{3hr}$	$\text{1}\text{.5hr}$	$\$200$

The manufacturer has $1200\text{hr}$ of labor available for assembly and $660\text{hr}$ labor available for painting.