Better Products, Inc., manufactures three products on two machines. In a typical week, $40$ hours are available on each machine. The profit contribution and production time in hours per unit are as follows:

Category Product $1$ Product $2$ Product $3$

Profit$/$unit $$39$ $$51$ $$18$

Machine $1$ time$/$unit $0\mathrm{.}51\mathrm{.}51$

Machine $2$ time$/$unit $12\mathrm{.}51$

Two operators are required for machine $1$; thus, $2$ hours of labor must be scheduled for each hour of machine $1$ time. Only one operator is required for machine $2.$ A maximum of $90$ labor$-$hours is available for assignment to the machines during the coming week. Other production requirements are that product $1$ cannot account for more than $50\%$ of the units produced and that product $3$ must account for at least $10\%$ of the units produced.

How many units of each product should be produced to maximize the total profit contribution? If required, round your answers to the nearest whole number. If your answer is zero, enter $0.$

Product # of units

$1$ fill in the blank $1$

$16$

$2$ fill in the blank $2$

$14$

$3$ fill in the blank $3$

$10$

What is the projected weekly profit associated with your solution?

Profit $=$ $ fill in the blank $4$

$1,518$

How many hours of production time will be scheduled on each machine?

Machine Hours Schedule:

Machine $1$ fill in the blank $5$

$39$

Hours

Machine $2$ fill in the blank $6$

$61$

Hours

What is the value of an additional hour of labor? If required, round your answer to two decimal places.

$ fill in the blank $7$

$5\mathrm{.}29$

Assume that labor capacity can be increased to $100$ hours. Develop the optimal product mix, assuming that the extra hours are made available. If required, round non$-$monetary answers to the nearest whole number. If required, round monetary answer to the nearest dollar. If your answer is zero, enter $0.$

Product # of units

$1$ fill in the blank $8$

$20$

$2$ fill in the blank $9$

$15$

$3$ fill in the blank $10$

$10$

Profit $=$ $ fill in the blank $11$

$1,725$

Would you be interested in using the additional $10$ hours available for this resource?