Barlow Company manufactures three products$-$A$,$ B$,$ and C$.$ The selling price, variable costs, and contribution margin for one unit of each product follow:

$\backslash$table$[[,$Product$],[,$A$,$B$,$C$,],[$Selling price,$$150,$$$240,$$$200,],[$Variable expenses:,,,,$],[,$ Direct materials,$12,48,18,],[$other variable expenses,$108,120,140,],[$Total variable expenses,$120,168,158,],[$Contribution margin,$$30,$$$72,$$$42,],[$Contribution margin ratio,$20\%,30\%,21\%,],[,,,,]]$

The same raw material is used in all three products. Barlow Company has only $5,400$ pounds of raw material on hand and will not be able to obtain any more of it for several weeks due to a strike in its supplier's plant. Management is trying to decide which product$($s$)$ to concentrate on next week in filling its backlog of orders. The material costs $$6$ per pound.

Required:

Calculate the contribution margin per pound of the constraining resource for each product.

Assuming Barlow has unlimited demand for each of its three products, what is the maximum contribution margin the company can earn when using the $5,400$ pounds of raw material on hand?

Assuming Barlow's estimated customer demand is $600$ units per product line, what is the maximum contribution margin the company can earn when using the $5,400$ pounds of raw material on hand?

A foreign supplier could furnish Barlow with additional stocks of the raw material at a substantial premium over the usual price. Assuming Barlow's estimated customer demand is $600$ units per product line and the company has used its $5,400$ pounds of raw material in an optimal fashion, what is the highest price Barlow Company should be willing to pay for an additional pound of materials?