A small engineering consulting firm has three senior designers available to work on

the firms four current projects over the next two weeks. Each designer has eighty

hours to split among the projects, and the following table shows the managers

scoring $(0=$ nil up to $100=$ perfect$)$ of the capability of each designer to contribute to

each project, along with an estimate of the hours that each project will require.

Designer Project

$1234$

$190801050$

$260705065$

$370408085$

Required hours $70508535$

$($i$)$ The manager wants to assign designers to maximize total capability. Formulate a

linear programming problem to help the manager.