uickbrush Paint Company is developing a linear program to determine the optimal quantities of ingredient A and ingredient B to blend together to make oil$-$base and water$-$base paint. The oil$-$base paint contains $90$ percent A and $10$ percent B$,$ whereas the water$-$base paint contains $30$ percent A and $70$ percent B$.$ Quickbrush currently has $10,000$ gallons of ingredient A and $5,000$ gallons of ingredient B in inventory and cannot obtain more at this time. Assuming that x represents the number of gallons of oil$-$base paint, and y represents the gallons of water$-$base paint, which constraint is correctly represents the constraint on ingredient A$?$

Group of answer choices

$\mathrm{.}3$x $+\mathrm{.}7$y $10,000$

$\mathrm{.}9$A $+\mathrm{.}1$B $10,000$

$\mathrm{.}9$x $+\mathrm{.}3$y $10,000$

$\mathrm{.}9$x $+\mathrm{.}1$y $10,000$

Boat

Variable Cost

Selling Price

Bass

$$12,500$

$$23,000$

Ski

$8,500$

$18,000$

Speed

$13,700$

$26,000$

The company has incurred fixed costs of $$2,800,000$ to set up its manufacturing operation and begin production. Lakeside has also entered into agreements with several boat dealers in the region to provide a minimum of $70$ bass boats, $50$ ski boats, and $50$ speedboats. Alternatively, the company is unsure of what actual demand will be$,$ so it has decided to limit production to no more than $120$ of any one boat. The company wants to determine the number of boats that it must sell to break even while minimizing its total variable cost.

Formulate a linear programming model for this problem.

Solve the model by using Solver in Excel