$3\mathrm{.}10.$ Consider a cost$-$benefit$-$trade$-$off problem having the following data.

Benefit Contribution per Unit of Each Activity

Benefit

$1$

$2$

$3$

$4$

Minimum

Acceptable

Level

Q

R

Unit cost

$2$

$1$

$3$

$$400$

$-1$

$4$

$5$

$$600$

$4$

$-1$

$4$

$$500$

$3$

$2$

$-1$

$$300$

$80$

$60$

$110$

a$.$ Formulate a linear programming model for this problem on a spreadsheet.

b$.$ Make five guesses of your own choosing for the optimal solution. Use the spreadsheet to check each one for feasibility and, if feasible, for the value of the objective function. Which feasible guess has the best objective function value?

c$.$ Use Solver to find an optimal solution.