Jenny owns a small pottery business where she makes and sells

hand$-$made pottery products for cash.

There are enough factors of production to meet the demand for the week except the labour hours.

At present she only works $45$ hours a week producing pottery products. She also serves customers in the shop.

The following information is available for the four pottery items produced and sold.

$$

The table shows information for one item of each product.

Product Pot Vase Mug Plate

Clay material used $($grams$)700$ g $500$ g $300$ g $600$ g

Labour time required $30$ minutes $15$ minutes $1$ hour $30$ minutes

Selling price $10\mathrm{.}706\mathrm{.}506\mathrm{.}8010\mathrm{.}00$

Material cost per unit $0\mathrm{.}700\mathrm{.}500\mathrm{.}400\mathrm{.}50$

Labour cost per unit $6336$

Weekly demand $($units$)20163012$

$$

Required

$$

$($a$)$ Calculate the total amount of kilogramme needed to produce the total weekly demand

$($units$).1000$ grams equals $1$ kilogram

$$

$($b$)$ Calculate the number of labour hours required to meet all the demand for all four

pottery products for one week.

$$

$($b$)$ Explain the term limiting factor.

$$

$($c$)$ Calculate the contribution for one item of each of the four pottery products.

$$

$($d$)$ Calculate the order of production of the four pottery products required to maximise

$$ profits each week.

$$

$($e$)$ Calculate the quantities of production of each pottery product that would maximise profit

$$ each week.

$$

The fixed cost for the month is $600.$ The business operates $4$ weeks for the month

$$

$($f$)$ Calculate the profit per week for Jenny$$s business.

Please show necessary working