Andy$$s Bicycle Company $($ABC$)$ has the hottest new product on the upscale toy market $$ boys$$ and girls$$ bikes in bright fashion colors, with oversize hubs and axles; shell design safety tires; strong padded frames; chrome$-$plated chains, brackets, and valves; and non$-$slip handlebars. Due to the seller$$s market for high$-$quality toys for the newest baby boomers, ABC can sell all the bicycles it manufactures at the following prices: boys$$ bikes, $$220$; girls$$ bikes, $$175.$ This is the price payable to ABC at its Orlando plant. The firm$$s accountant, V$.$ R$.$ Dondeti, has determined that direct labor costs will be $45\%$ of the price that ABC receives for the boys$$ model and $40\%$ of the price received for the girls$$ model. Production costs, other than labor but excluding painting and packaging, $$44$ per boys$$ bicycle and $$30$ per girls$$ bicycle. Painting and packaging are $$20$ per bike, regardless of model. The Orlando plant$$s overall production capacity is $390$ bicycles per day. Each boys$$ bike requires $2\mathrm{.}5$ labor$-$hours, each girls$$ model $2\mathrm{.}4$ hours. ABC currently employs $120$ workers, each of whom puts in an $8-$hour day. The firm has no desire to hire or fire to affect labor availability, for it believes its stable workforce is one of its biggest assets.

a$.$ What is the product allocation?

$240$ boys and $150$ girls

b$.$ What is the total profit?

$$21,930\mathrm{.}00$

c$.$ Are there any unused resources?

no

d$.$ What if you decided to reduce hours by $22,$ what impact would it have on profit?

profit would be reduced by $$440$

e$.$ Reverting back to the original $120$ employees working $8$ hours a day. What if the company decided to layoff $($because of supply chain issues$)2$ employees working the same amount of hours$/$per day, what impact would it have on resource allocation and profits?