2 ) Four products ( A , B , C and D ) are produced using three inputs ( Gaskets , Valves and Fasteners )

$2)$ Four products $($A$,$ B$,$ C and D$)$ are produced using three inputs $($Gaskets$,$ Valves and Fasteners$).$ The profit margin and demand for each product is provided in table one, table two provides number of each input needed to make a unit of each product, as well as aggregate requirements $($based on demand$)$ and available capacity.

Table One

Product A

Product B

Demand

$$\mathrm{2.50}$

$\mathrm{125}$

Product C

$$\mathrm{2.95}$

$\mathrm{150}$

Product D

$$\mathrm{3.00}$

$$\mathrm{4.00}$

$\mathrm{110}$

$\mathrm{200}$

Profit$/$Unit

Table Two

#of inputs needed per unit of product

Product A

Product B

Product C

Product D

Available Capacity

Gaskets

$6$

$5$

Valves

Fasteners

Aggregate Workload

$4$

$5$

$2$

$3$

$\mathrm{2780}$

$\mathrm{5000}$

$\mathrm{2620}$

$\mathrm{11}$

$\mathrm{14}$

$\mathrm{12}$

$\mathrm{12}$

$7$

$\mathrm{1700}$

$\mathrm{7195}$

$\mathrm{7200}$

Note that they only have $1,\mathrm{700}$ Valves$-$not nearly enough to meet all of demand for all four products $($Gaskets and Fasteners are in adequate supply$).$ If the company were to determine the "product mix" that maximizes profit, how many units of product B would that include? full marks for this question requires that work be shown

The optimal product mix would include units of product B$.$