A supplier supplies 50 T-shirts when the price is R60 per t-shirt and 90 t-shirts when the price is R110 per t-shirt.
a). Determine the equation of the supply function as a function of q?
b). How many additional t-shirts are sopplied for each successive R1 increase in price?
c). How many t-shirts are sopplied when the price is R85?
d). What is the price when 120 t-shirts are sopplied?
a)Supply equation is written as;
"P_{s}=mQ+b"
where m is the slope of supply curve.
m="\\frac{\\delta P}{\\delta Q}=\\frac{110-60}{90-50}=1.25"
Inserting the supply of 50 T-shirts at a price of R60 per t-shirt in the supply equation to get b;
"60=1.25\\times50+b"
"b=-2.5"
"\\therefore" the supply equation becomes;
"P_{s}=1.25Q-2.5"
b). Additional t-shirts supplied for each successive R1 increase in price will be?
For every R1 increase in price;
"1=1.25Q-2.5"
"Q=\\frac{3.5}{1.25}=2.8"
c) T-shirts supplied when the price is R85;
"85=1.25Q-2.5"
"Q=\\frac{87.5}{1.25}=70" t-shirts
d) Price when 120 t-shirts are supplied;
"P_{s}=1.25Q-2.5"
"P_{s}=1.25\\times120-2.5=R147.5"
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