A cycle tyre manufacturing company has been approached by a large shopkeeper that offers to buy

$10\mathrm{.}000$ tyres at $\text{'}3,200.$ Delivery must be made within $30$ days. The production capacity of the company is

$64\mathrm{.}000$ units per month and there is inventory of $2000$ tyres. Expected sales at regular prices for the

coming month are $60\mathrm{.}000$ tyres. It is estimated by the sales manager that about $50\%$ of sales lost during

the month would bee made up in later months. Price and cost data per unit are a fallow.... sales lost ding

required: $$

$($a$)$ Determine whether the offer should be accepted or not.

$($b$)$ Determine the lowest price that the company could charge on the special order and not reduce its

income.

$($c$)$ Suppose now that the shopkeeper offers to buy $8\mathrm{.}000$ tyres per month at $3200$ per lyre. The offer

would be for an entire year. Expected sales are $60\mathrm{.}000$ tyres per month without accepting the special

order. Assuming further that there is no beginning inventory and that sales lost during the year would not

made th in the following year determine whether the offer should be aceepted and determine the

owest price that company could accept.