Part I $$ Component Manufacturing $(3$ points$)$

Vollmer Manufacturing makes three components for sale to refrigeration companies. The components are processed on two machines: a shaper and a grinder. The times $($in minutes$)$ required on each machine are as follows:

Component

Shaper

Grinder

$1$

$4$

$4$

$2$

$8$

$5$

$3$

$4$

$2$

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The shaper is available for $120$ hours, and the grinder for $110$ hours. No more than $200$ units of component $3$ can be sold, but up to $1,000$ units of each of the other components can be sold. In fact, the company already has orders for $600$ units of component $1$ that must be satisfied. The per unit profit $($in dollars$)$ for each of the three components are as follows:

Component

Profit Margin

$1$

$9$

$2$

$6$

$3$

$9$

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a$.$ Formulate and solve for the recommended production quantities that will maximize contribution to profit. In other words, determine the number of components $1,2,$ and $3$ to produce such that the total profit is maximized. No mathematical model is required. Only the Excel model and solution is required. $(2$ points$)$

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b$.$ If one more hour could be made available on the shaper, how much would it be worth? $(1$ point$)$