The XYZ Company produces two products. The total profit achieved from these prod$-$

ucts is described by the following equation:

Total profit $=-0\mathrm{.}2x_1^2-0\mathrm{.}4x_2^2+8x_1+12x_2+1500$

where $x_1=$ thousands $of$ units $of$ product $1$

$x_2=$ thousands $of$ units $of$ product $2$

Every $1,000$ units of $x_1$ requires one hour of time in the shipping department, and every

$1,000$ units of $x_2$ requires $30$ minutes in the shipping department. Each unit of each

product requires two pounds of a special ingredient, of which $64,000$ pounds are avail$-$

able. Additionally, $80$ hours of shipping labor are available. Demand for $x_1$ and $x_2$ is

unlimited.

a$.$ Formulate an NLP model for this problem.

b$.$ Implement your model in a spreadsheet and solve it$.$

c$.$ What is the optimal solution?