Please show your work, step by step. $5\mathrm{.}11.$ The WorldLight Company produces two light fixtures $($Products $1$ and $2)$ that require both metal frame parts and electrical components. Management wants to determine how many units of each product to produce per week so as to maximize profit. For each unit of Product $1,$ one unit of frame parts and two units of electrical components are required. For each unit of Product $2,$ three units of frame parts and two units of electrical components are required. The company has a weekly supply of $3,000$ units of frame parts and $4,500$ units of electrical components. Each unit of Product $1$ gives a profit of $\backslash (\backslash$$ $13\backslash ),$ and each unit of Product $2,$ up to $900$ units, gives a profit of $\backslash (\backslash$$ $26\backslash ).$ Any excess over $900$ units of Product $2$ brings no profit, so such an excess has been ruled out.

a$.$ Identify verbally the decisions to be made, the constraints on these decisions, and the overall measure of performance for the decisions.

b$.$ Convert these verbal descriptions of the constraints and the measure of performance into quantitative expressions in terms of the data and decisions.

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

$\backslash ($ d $\backslash ).$ Formulate this same model algebraically.