Table $10-8$

A haberdashery produces scarves, ascots, and capes.

The haberdashery makes $$5$ profit for each scarf, $$3$ for

an ascot, and $$4$ for a cape. In addition, they are able to

enjoy some economies of scale if the batch exceeds one

scarf, ascot, or cape so they always make at least two

consecutive units of each item. For a scarf, the

additional profit is $1\mathrm{.}2S^2$; for an ascot, the profit made

by making consecutive items results in an extra $1\mathrm{.}5A^2$;

and for a cape, the bump is $2\mathrm{.}2C^2.$ There is also a little

extra profit due to the synergy of the scarves, ascots, and

capes that adds an additional $3$SAC. It takes $15$ minutes

to produce a scarf, $12$ minutes to produce an ascot and

$20$ minutes to produce a cape. There is a total of $80$

hours available for labor each week. There must be at

least $25$ scarves and $35$ capes produced each week.

Use Solver to determine the optimal product mix for the

scenario described in Table $10-8.$

$106$ scarves, $134$ ascots, $80$ capes

$50$ scarves, $100$ ascots, $50$ capes

$88$ scarves, $100$ ascots, $74$ capes

$75$ scarves, $100$ ascots, $25$ capes